Curriculum Vitae of Yaozhong HU

Transcription

1 Curriculum Vitae of Yaozhong HU A. List of submitted papers 1. (with Chen, L. and Nualart, D.) Regularity and strict positivity of densities for the nonlinear stochastic heat equation. Submitted. 2. Itô type stochastic differential equations driven by fractional Brownian motions of Hurst parameter H > 1/2. Submitted. 3. (with Khoa Le) Asymptotics of the density of parabolic Anderson random fields. Near completion. 4. (with Han, Z. and Lee, C.) On the linear-quadratic control in a regulated market via reflected diffusions. Ready for submission. 5. (with Han, Z. and Lee, C.) On the pricing barrier control in a regime-switching regulated market. Submitted. 6. (with Cheng, Y. and Long, H.) Generalized moment estimation for Ornstein-Uhlenbeck processes driven by α-stable Lévy motions from discrete time observations. Near completion. 7. (with Cheng, Y.; Ghoddusi, H. and Lee, C.) Optimal Adjustment of Energy Prices. Near completion. 8. (with Nualart, D. and Zhou, H.) Parameter estimation for fractional Ornstein-Uhlenbeck processes of general Hurst parameter. Ready to submit. 9. (with Chen, X.; Song, J. and Song, X.) Temporal asymptotics for fractional parabolic Anderson model. Submitted. 10. (with G. Rang) Parameter Estimation For Stochastic Hamiltonian Systems Driven By Fractional Brownian Motions. 11. (with Chen, X. and Song, J.) Feynman-Kac formula for fractional heat equation driven by fractional white noise. Submitted. 1

2 B. List of refereed publications 12. (with Chen, X.; Nualart, D. and Tindel, S.) Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise. To appear in Electronic Journal of Probability. 13. (with B. Øksendal and A. Sulem) Singular mean-field control games. Stoch. Anal. Appl. 35 (2017), no. 5, (with Nualart, D. and Zhang, T.) Large deviations for stochastic heat equation with rough dependence in space. To appear in Bernoulli. 15. (with Chen, L.; Kalbasi, K. and Nualart, D.) Intermittency for the stochastic heat equation driven by time-fractional Gaussian noise with H (0, 1/2). To appear in Prob. Theory and Related Fields. 16. (with Chen, L. and Nualart, D.) Two-point correlation function and Feynman-Kac formula for the stochastic heat equation. Potential Anal. 46 (2017), no. 4, (with Le, K. and Mytnik, L.) Stochastic differential equation for Brox diffusion. Stochastic Process. Appl. 127 (2017), no. 7, (with J. Huang, Le, K. and Nualart, D. and Tindel, S.) Stochastic heat equation with rough dependence in space. To appear in Annals of Probability. 19. Analysis on Gaussian spaces. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, xi+470 pp. 20. (With Chen, L.; Hu, G. and Huang, J.) Space-time fractional diffusions in Gaussian noisy environment. Stochastics 89 (2017), no. 1, (with Huang, J. and Nualart, D.) On the intermittency front of stochastic heat equation driven by colored noises. Electron. Commun. Probab. 21 (2016), Paper No. 21, 13 pp. 22. (with Le, K.) Nonlinear Young integrals and differential systems in Hölder media. Trans. Amer. Math. Soc. 369 (2017), no. 3, (with Y. Liu and D. Nualart) Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions. Ann. Appl. Probab. 26 (2016), no. 2, (with Le, K.) Nonlinear Young integrals via fractional calculus. Stochastics of environmental and financial economics-centre of Advanced Study, Oslo, Norway, , 81-99, Springer Proc. Math. Stat., 138, Springer, Cham, (with Liu, Y. and Nualart, D.) Taylor schemes for rough differential equations and fractional diffusions. Taylor schemes for rough differential equations and fractional diffusions. Discrete Contin. Dyn. Syst. Ser. B 21 (2016), no. 9, (with Han, Z. and Lee, C.) Optimal pricing barriers in a regulated market using reflected diffusion processes. Quant. Finance 16 (2016), no. 4, (with Hu, G.) Fractional diffusion in Gaussian noisy environment. Mathematics 2015, 3, ; doi: /math

3 28. (with Lee, C.; Lee, M. H. and Song, J.) Parameter estimation for reflected Ornstein-Uhlenbeck processes with discrete observations. Stat Inference Stoch Process 18 (2015), (with Chen, X., Song, J. and Xing, F.) Exponential asymptotics for time-space Hamiltonians. Annales de l Institut Henri Poincaré - Probabilités et Statistiques Vol. 51 (2015), No. 4, (With Huang, J.; Nualart, D. and Sun, X.) Smoothness of the joint density for spatially homogeneous SPDEs. J. Math. Soc. Japan 67 (2015), no. 4, (with Huang, J.; Nualart, D. and Tindel, S.) Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency. Electron. J. Probab. 20 (2015), no. 55, 50 pp. 32. (with J. Huang and D. Nualart) On Hölder continuity of the solution of stochastic wave equations in dimension three. Stoch. Partial Differ. Equ. Anal. Comput. 2 (2014), no. 3, (with Nualart, D.; Tindel, S. and Xu, F.) Density convergence in the Breuer-Major theorem for Gaussian stationary sequences. Bernoulli 21 (2015), no. 4, (with F. Lu and D. Nualart) Convergence of densities of some functionals of Gaussian processes. J. Funct. Anal. 266 (2014), no. 2, (with D. Nualart and F. Xu) Central limit theorem for an additive functional of the fractional Brownian motion. Ann. Probab. 42 (2014), no. 1, (with Nualart, D. and Song, J.) The 4 3-variation of the derivative of the self-intersection Brownian local time and related processes. J. Theoret. Probab. 27 (2014), no. 3, (with G. Rang) Identification of the point sources in some stochastic wave equations. Abstr. Appl. Anal. 2014, Art. ID (with Le, Khoa) A multiparameter Garsia-Rodemich-Rumsey inequality and some applications. Stochastic Process. Appl. 123 (2013), no. 9, (with F. Lu and D. Nualart) Non-degeneracy of some Sobolev pseudo-norms of fractional Brownian motion. Electron. Commun. Probab. 18 (2013), no. 84, 8 pp. 40. (with Y. Han and J. Song) Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions. Appl. Math. Optim. 67 (2013), no. 2, (with C. Lee) Drift parameter estimation for a reflected fractional Brownian motion based on its local time. J. Appl. Probab. 50 (2013), no. 2, (with J. Song) Parameter estimation for fractional Ornstein-Uhlenbeck processes with discrete observations. In Malliavin calculus and stochastic analysis, , Springer Proc. Math. Stat., 34, Springer, New York, (with D. Nualart and J. Song) A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution. Stochastic Process. Appl. 123 (2013), no. 3, (with F. Biagini, T. Meyer-Brandis and B. Øksendal) Insider trading equilibrium in a market with memory. Math. Financ. Econ. 6 (2012), no. 3,

4 45. Multiple integrals and expansion of solution to differential equations driven by rough path and by fractional Brownian motion. Stochastics 85 (2013), no. 5, (with F. Lu and D. Nualart) Hölder continuity of the solutions for a class of nonlinear SPDE s arising from one dimensional superprocesses. Probab. Theory Related Fields 156 (2013), no. 1-2, (with Jolis M. and Tindel S.) On Stratonovich and Skorohod stochastic calculus for Gaussian processes. Annals of Probability 41 (2013), no. 3A, (with S. Tindel) Smooth Density for Some Nilpotent Rough Differential Equations. J. Theoret. Probab. 26 (2013), no. 3, Stochastic quantization and ergodic theorem for diffusion processes. Sci. China Math. 55 (2012), no. 11, (with D. Ocone and J. Song) Some results on backward stochastic differential equations driven by fractional Brownian motions. in Stochastic Analysis and Applications to Finance. Essays in honor of Jia-An Yan. World Scientific Publishing Co. 2012, (with C. Yang) Optimal tracking for bilinear stochastic system driven by fractional Brownian motions. J. Syst. Sci. Complex. 25 (2012), no. 2, (with D. Nualart and F. Lu) Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter H < 1/2. Ann. Probab. 40 (2012), no. 3, (with Nualart, D.; Xiao, W. and Zhang, W.) Exact maximum likelihood estimator for drift fractional Brownian motion at discrete observation. Acta Math. Sci. Ser. B Engl. Ed. 31 (2011), no. 5, An enlargement of filtration for Brownian motion. Acta Math. Sci. Ser. B Engl. Ed. 31 (2011), no. 5, (with D. Nualart and X. Song) Malliavin calculus for backward stochastic differential equations and application to numerical schemes. The Annals of Applied Probability Vol. 21 (2011), (with D. Nualart and J. Song) Feynman-Kac formula for heat equation driven by fractional white noise. The Annals of Probability 39 (2011), no. 1, (with D. Nualart) Central limit theorem for the third moment in space of the Brownian local time increments. Electron. Commun. Probab. 15 (2010), (with D. Nualart) Parameter estimation for fractional Ornstein-Uhlenbeck processes. Statist. Probab. Lett. 80 (2010), no , (with B. Wang) Convergence rate of an approximation to multiple integral of fractional Brownian motion. Acta Math. Sci. Volume 30 (2010), A random transport-diffusion equation. Acta Math. Scientia. Vol 30 (2010), (with D. Nualart and J. Song ) Fractional martingales and characterization of the fractional Brownian motion. Ann. Probab. 37 (2009), no. 6, (with D. Nualart) Stochastic integral representation of the L 2 modulus of Brownian local time and a central limit theorem. Electron. Commun. Probab. 14 (2009),

5 63. (with J.A. Yan) Wick calculus for nonlinear Gaussian functionals. Acta Math. Appl. Sin. Engl. Ser. 25 (2009), no. 3, (with Long H. W.) Least squares estimator for Ornstein-Uhlenbeck processes driven by α-stable motions. Stochastic Process. Appl. 119 (2009), no. 8, (with Long H. W.) On the singularity of least squares estimator for mean-reverting α-stable motions. Acta Math. Sci. Ser. B Engl. Ed. 29 (2009), no. 3, (with S. Peng) Backward stochastic differential equations driven by fractional Brownian motion. SIAM Journal of Control and Optimization, 48 (2009), (with D. Nualart and J. Song ) Integral representation of renormalized self-intersection local times. J. Funct. Anal. 255 (2008), no. 9, (with D. Nualart and X. Song ) A singular stochastic differential equation driven by fractional Brownian motion. Statist. Probab. Lett. 78 (2008), no. 14, (with B. Øksendal) Partial information linear quadratic control for jump diffusions. SIAM Journal of Control and Optimization, 47 (2008), (with B. Øksendal) Optimal anticipative stopping. Advances in Math. of Finance (L. Stettner ed.). Banach Center Publications vol. 83 (2008), (with D. Nualart) Rough path analysis via fractional calculus. Trans. Amer. Math. Soc. 361 (2009), no. 5, (with D. Nualart) Stochastic heat equation driven by fractional noise and local time. Prob. Theory and Related Fields, 143 (2009), (with B. Øksendal) Optimal smooth portfolio selection for an insider. J. Appl. Probab. 44 (2007), no. 3, (with Biagini, F. B. Øksendal and Zhang, T.S.) Stochastic calculus for fractional Brownian motion and applications. Probability and its Applications (New York). Springer-Verlag London, Ltd., London, (with D. Nualart) Regularity of renormalized self-intersection local time for fractional Brownian motion. Communications in Information and Systems, 7 (2007), (with D. Nualart) Differential equation driven by Hölder continuous functions of order greater than 1/2. in The Abel Symposium on Stochastic Analysis, Springer, (with H. Long) Parameter estimation for Ornstein-Uhlenbeck processes driven by α-stable Lévy motions. Communications on Stochastic Analysis, 1 (2007), (with Mohammed, S., Arritojas, M. and Pap, G.) A Delayed Black and Scholes Formula, Stoch. Anal. Appl. 25 (2007), no. 2, Integral transformations and anticipative calculus for fractional Brownian motions. Mem. Amer. Math. Soc. 175 (2005), no. 825, viii+127 pp. 80. (with Øksendal, B. and Salopek, D. M.) Weighted local time for fractional Brownian motion and applications to finance. Stoch. Appl. Anal. 23 (2005), no. 1,

6 81. (with Zhou X.Y.) Stochastic control for linear systems driven by fractional noises. SIAM J. Control Optim. 43 (2005), no. 6, Optimization of portfolio and consumption and minimization of volatility. Mathematics of finance, , Contemp. Math., 351, Amer. Math. Soc., Providence, RI, (with D. Nualart) Renormalized self-intersection local time for fractional Brownian motion. Ann. Probab. 33 (2005), no. 3, (with D. Nualart) Some processes associated with fractional Bessel processes. J. Theoret. Probab. 18 (2005), no. 2, (with B. Øksendal and A. Sulem) Optimal portfolio in a fractional Black-Scholes market driven by fractional Brownian motion. Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 6 (2004), (with S. E. A. Mohammed and F. Yan) Numerical Solution of Stochastic Differential Systems with Memory. Annals of Probability, 32 (2004), Optimal consumption and portfolio in a market where the volatility is driven by fractional Brownian motion. Probability, Finance and Insurance. Ed. Lai, T.L. et al. World Scientific Publishing (with Øksendal and T. S. Zhang) General fractional multiparameter white noise theory and stochastic partial differential equations, Communications in partial differential equations 29 (2004), (with B. Øksendal) Fractional white noise calculus and applications to finance. Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 6 (2003), (with F. Biagini, B. Øksendal and A. Sulem) A Stochastic maximum principle for processes driven by fractional Brownian motion, Stochastic Processes and Applications, 100 (2002), (with G. Kallianpur, J. Xiong) An approximation for Zakai equation, Applied Mathematics and optimization 45 (2002), no. 1, Probability structure preserving and absolute continuity, Annales de l Institut Henri Poincaré, 38 (2002), no. 4, (with Üst nel, A. S.; Zakai, M.) Tangent processes on Wiener space. J. Funct. Anal. 192 (2002), no. 1, Chaos expansion of heat equation with white noise potentials, Potential Anal. 16 (2002), no. 1, (with Øksendal, B.) Chaos expansion of local time of fractional Brownian motions. Stochastic Anal. Appl. 20 (2002), no. 4, Self-intersection local time of fractional Brownian motions - via chaos expansion, Journal of Mathematics of Kyoto University, 41 (2001), no. 2, Heat equation with fractional white noise potentials, Applied Mathematics and Optimization, 43 (2001), (with Øksendal and T. S. Zhang) Stochastic fractional potential theory, Papers in Analysis, Report. Univ. Jyväskylä, 83 (2001),

7 99. Option pricing in a market where the volatility is driven by fractional Brownian motions, Recent Development in Mathematical Finance. Ed. J.M. Yong. World Scientific. 2002, Prediction and translation of fractional Brownian motions, Stochastics in Finite and Infinite Dimensions, Ed. T. Hida et al., Trends Math., Birkhäuser, Boston, MA, 2001, (with Duncan, T. E. and Pasik-Duncan, B.) Stochastic calculus for fractional Brownian motion. I. Theory. SIAM J. Control Optim. 38 (2000), no. 2, (with G. Kallianpur) Schrodinger equations with fractional Laplacians, Applied Mathematics and Optimization, 42 (2000), Optimal times to observe in the Kalman-Bucy models, Stochastics and Stochastics Report, 69 (2000), Multi-dimensional geometric Brownian motions, Onsager-Machlup functions, and applications to mathematical finance, Acta Math. Sci. 20 (2000), (with B. Øksendal and T. Zhang) Stochastic partial differential equations driven by multi-parameter fractional white noise, Stochastic Processes, Physics and Geometry: New Interplays. II, Ed. F. Gesztesy et al., AMS 2000, A unified approach to several inequalities for Gaussian and diffusion measures, Séminaire XXXIV, Lecture Notes 1729, Springer-Verlag, 2000, A Class of stochastic partial differential equations driven by fractional white noises, Stochastic Processes, Physics and Geometry: New Interplays. II, Ed. F. Gesztesy et al., AMS 2000, (with B. Øksendal and A. Sulem) Optimal portfolio in a fractional Black-Scholes market, Mathematical Physics and Stochastic Analysis, Ed. S. Albeverio et al., World Scientific 2000, (with R.J. de Figuereido) On non-linear filtering of non-gaussian processes through Volterra series, Volterra Equations and Applications, Arlington, TX, 1996, , Stability Control Theory Methods Appl., 10, Gordon and Breach, Amsterdam, (with S. Albeverio, M. Rockner and X.Y. Zhou) Stochastic quantization of the two-dimensional polymer measure, Applied Mathematics and Optimization, 40 (1999), Exponential integrability of diffusion processes, Advances in Stochastic Inequalities, Ed. T.P. Hill and C. Houdré, Contemporary Mathematics, 234 (1999), American Mathematical Society, 1999, On the positivity of the solution of a class of stochastic pressure equations, Stochastics and Stochastics Reports, 63 (1998), (with B. Øksendal) Optimal time to invest when the price processes are geometric Brownian motions, Finance and Stochastics, 2 (1998), Itô-Wiener chaos expansion with exact residual and correlation, variance inequalities, Journal of Theoretical Probability, 10 (1997), (with Z. Q. Chen, Z. M. Qian and W. A. Zheng) Stability and approximations of symmetric diffusion semigroups and kernels, Journal of Functional Analysis, 152 (1998), (with D. Nualart) Continuity of some anticipating integral processes, Statistics and Probability Letters, 37 (1998),

8 117. (with G. Kallianpur) Exponential integrability and application to stochastic quantization, Applied Mathematics and Optimization, 37 (1998), (with S.Albeverio and X.Y. Zhou) A remark on non smoothness of self-intersection local time of planar Brownian motion, Statistics and Probability Letter, 32 (1997), (with H. Holden) Finite difference approximation of the pressure equation for fluid flow in a stochastic medium a probabilistic approach, Comm. Partial Differential Equation, 21 (1996), On the self-intersection local time of Brownian motion-via chaos expansion, Publ. Mat., 40 (1996), (with Bruce K. Driver) On heat kernel logarithmic Sobolev inequalities, Stochastic Analysis and Applications (Powys, 1995), World Sci. Publishing, River Edge, NJ, 1996, Strong and weak order of time discretization schemes of stochastic differential equations, Séminaire de Probabilités XXX, Ed. J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1626, Springer-Verlag, 1996, (with S. Watanabe) Donsker s delta functions and approximation of heat kernels by time discretization methods, J. Math. Kyoto University, 36 (1996), (with S. Cambanis) The exact convergence rate of Euler-Maruyama scheme and application to sample design, Stochastics and Stochastics Reports, 59 (1996), Semi-implicit Euler-Maruyama scheme for stiff stochastic equations, Stochastic Analysis and Related Topics, V (Silivri, 1994), Progr. Probab., 38, Birkhäuser Boston, Boston, MA, 1996, (with B. Øksendal) Wick approximation of quasilinear linear stochastic differential equations, Stochastic Analysis and Related Topics, Progr. Prob. 38, Birkhäuser, Boston, 1996, (with T. Lindstrøm, B. Øksendal, J. Ubøe and T.S. Zhang) Inverse power of white noise, Proc. Symp. Pure Math. 57 (1995), (with V. Peres-Abreu) On the continuous extension of Wiener chaos, Bol. Soc. Mat. Mexicana, 1, (1995), On the differentiability of functions of an operator, Séminaire de Probabilités XXIX, Ed. J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1613, Springer-Verlag, 1995, The pathwise solution for a class of quasilinear stochastic equations of evolution in Banach space II, Acta Mathematica Scientia, 15 (1995), Some operator inequalities, Séminaire de Probabilités XXVIII, Ed. by J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1583, Springer-Verlag, 1994, The pathwise solution for a class of quasilinear stochastic equation of evolutions in Banach spaces I, Acta Mathematica Scientia, 14 (1994), (with P.A.Meyer) On the approximation of Stratonovitch multiple integrals, Stochastic Processes, a festschrift in honor of G. Kallianpur, Ed. S. Cambanis et al., Springer, 1993,

9 134. ( with Long Hongwei) Symmetric integral and the approximation theorem of stochastic integral in the plane, Acta Mathematica Scientia, 13 (1993), A remark on the value on zero of a Brownian functional, Stochastic Analysis and Related Topics, Proc. Fourth Oslo-Silivri Workshop on Stochastic Analysis, Ed. T. Lindstrøm, B. Øksendal and A.S. Üstünel, Gordon and Breach Science Publishers, 1993, (with L. Decreusefond, A.S. Üstünel) Une inégalité d interpolation sur l espace de Wiener, Compte Rendus Acad. Sci. Paris, 317 (1993), Hypercontractivité pour les fermions, d aprés Carlen-Lieb, Séminaire de Probabilités XXVII, Ed. J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1557, Springer-Verlag, 1993, The pathwise solutions for a class of quasi-linear stochastic equations of evolution in Banach spaces III, Acta Mathematica Scientia, 13 (1993), Sur un travail de R. Carmona et D. Nualart, Séminaire de Probabilités XXVI, Ed. J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1526, Springer-Verlag, 1992, Une formule d Itô pour le mouvement Brownien fermionique, Séminaire de Probabilités XXVI, Ed. J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1526, Springer-Verlag, 1992, Une remarque sur l inégalité de Hölder non-commutative, Séminaire de Probabilités XXVI, ed. J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1526, Springer-Verlag, 1992, Calculation of Feynman path integral for certain central forces, Stochastic Analysis and Related Topics (Oslo, 1992), Stochastics Monogr., 8, Gordon and Breach, Montreux, 1993, Série de Taylor stochastique et formule de Campbell-Hausdorff - d apès Ben Arous, Séminaire de Probabilités XXVI, Ed. J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1526, Springer-Verlag, 1992, Existence de traces dans les développements en chaos de Wiener. Dissertation, Université Louis Pasteur, Strasbourg, Publication de l Institut de Recherche Mathématique Avancée, 480. Université Louis Pasteur, Département de Mathématique, Institut de Recherche Mathématique Avancée, Strasbourg, pp Calculs formels sur les e.d.s. de Stratonovitch, Séminaire de Probabilités XXVI, Ed. J. Azema, P.A. Meyer and M. Yor, Lect. Notes in Math. 1426, Springer-Verlag, 1990, Symmetric integral and canonical extension for jump process - some combinatorial results, Acta Math. Sci. 10, (1990), Some notes on multiple Stratonovitch integrals, Acta Math. Sci. 9 (1989), Un nouvel exemple de distribution de Hida, Séminaire de Probabilités XXVI, Ed. J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1321, Springer-Verlag, 1988, (with P.A.Meyer) Chaos de Wiener et intégrales de Feynman, Séminaire de Probabilités XXII, Ed. J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1321, Springer-Verlag, 1988,

10 150. (with P.A.Meyer) Sur les intégrales multiples de Stratonovitch, Séminaire de Probabilités XXVI, Ed. J. Azema, P.A. Meyer and M. Yor, Lecture Notes in Mathematics 1321, Springer-Verlag, 1988, Stochastic analysis of the stochastic functional on the basic space, Acta Math. Sci. 6 (1986), pp