Huaizhong Zhao, Department of Mathematical Sciences, Loughborough University

Preprints

[64] Qi Zhang and Huaizhong Zhao, SPDEs with Polynomial Growth Coefficients and Malliavin Calculus Method, submitted.

[63] Lifeng Wei, Zhen Wu and Huaizhong Zhao, Dynamical programming principle for stochastic relaxed control problems and Hamilton-Jacobi-Bellman equations, submitted.

Publications

[62] Qi Zhang and Huaizhong Zhao, Probabilistic representation of weak solutions of partial differential equations with polynomial growth coefficients, Journal of Theoretical Probability, Vol. 25 (2012), 396-423. doi: 10.1007/s10959-011-0350-y

[61] Chunrong Feng and Huaizhong Zhao, Random Periodic Solutions of SPDEs via Integral Equations and Wiener-Sobolev Compact Embedding, Journal of Functional Analysis, Vol. 262 (2012), 4377-4422. http://dx.doi.org/10.1016/j.jfa.2012.02.024

[60] New Trends in Stochastic Analysis and Related Topics—a volume in honour of Professor K.D. Elworthy, edited by Huaizhong Zhao and Aubrey Truman, Interdisciplinary Mathematical Sciences—Vol. 12, World Scientific, 2012. ISBN: 978-981-4360-91-3. Publication information see the Publisher webpage

[59] Peng Lian and Huaizhong Zhao, Pathwise properties of random mappings, In: New Trends in Stochastic Analysis and Related Topics—a volume in honour of Professor K.D. Elworthy, edited by H.Z. Zhao and A. Truman, World Scientific, 2012, pp. 227-300.

[58] Chunrong Feng, Huaizhong Zhao and Bo Zhou, Pathwise random periodic solutions of stochastic differential equations, Journal of Differential Equations, Vol. 251 (2011), 119-149. doi:10.1016/j.jde.2011.03.019 

[57] Andrei Yevik and Huaizhong Zhao, Numerical approximation to the stationary solutions of stochastic differential equations, SIAM Journal on Numerical Analysis, Vol. 49 (2011), 1397-1416.

[56] Chunrong Feng and Huaizhong Zhao, Local time rough path for Levy processes, Electronic Journal of Probability, Vol. 15 (2010), 452-483.

[55] Qi Zhang and Huaizhong Zhao, Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients, Journal of Differential Equations, Vol. 248 (2010), 953-991. doi:10.1016/j.jde.2009.12.013

[54] Yong Liu and Huaizhong Zhao, Representation of pathwise stationary solutions of stochastic Burgers equations, Stochastics and Dynamics, Vol. 9 (2009), 613-634.

[53] Huaizhong Zhao and Zuohuan Zheng, Random periodic solutions of random dynamical systems, Journal of Differential Equations, Vol. 246 (2009), No. 5, 2020-2038. doi:10.1016/j.jde.2008.10.011.

[52] Chunrong Feng and Huaizhong Zhao, Rough path integral of local time, C. R. Acad. Sci. Paris, Ser. I 346 (2008), 431-434. doi:10.1016/j.crma.2008.02.015.

[51] Salah-Eldin A. Mohammed, Tusheng Zhang and Huaizhong Zhao, The stable manifold theorem for semilinear stochastic evolution equations and stochastic partial differential equations, Memoirs of the American Mathematical Society, Vol. 196 (2008), No. 917, 1-105.

[50] Shaolin Ji and Huaizhong Zhao, On the solvability of forward-backward stochastic differential equations with absorption coefficients, Chinese Annals of Mathematics, Series A, Vol. 29A(1)(2008), 71-82.

[49] Chunrong Feng and Huaizhong Zhao, A Generalized Ito's Formula in Two-Dimensions and Stochastic Lebesgue-Stieltjes Integrals, Electronic Journal of Probability, Vol. 12 (2007), 1568-1599. 

[48] Qi Zhang and Huaizhong Zhao, Stationary solutions of SPDEs and infinite horizon BDSDEs, Journal of Functional Analysis,Vol. 252 (2007), 171-219.  (DOI: 10.1016/j.jfa.2007.06.019)

[47] K. D. Elworthy, A. Truman and H.Z. Zhao, A generalized Ito formula and space-time Lebesgue-Stieltjes integrals of local times, Seminaire de Probabilites, Vol.40 (2007), 117-136. (DOI: 10.1007/978-3-540-71189-6_5)

[46] Chunrong Feng and Huaizhong Zhao, Two-parameter p,q-variation paths and integrations of local times, Potential Analysis, Vol. 25 (2006), 165-204.

[45] Dongmei Guo, Shaolin Ji and Huaizhong Zhao, On the solvability of infinite horizon forward-backward stochastic differential equations with absorption coefficients , Statistics and Probability Letters, Vol.76 (2006), 1954-1960.

[44] I. M. Davies, A. Truman and H.Z. Zhao, Stochastic heat and Burgers equations and their singularities II-analytic properties and limiting distributions, Journal of Mathematical Physics, Vol. 46, No. 4, article No. 043515, 31 pages, 2005.

[43] I. M. Davies, A. Truman and H.Z. Zhao, Stochastic heat and Burgers equations and their singularities, IMA Volumes in Mathematics and its Applications, Vol. 140, Springer-Verlag, 2005, pp 75-92.

[42] I. M. Davies, A. Truman and H.Z. Zhao, Stochastic heat and Burgers equations and the intermittence of turbulence, Progress in Probability, 58 (2004), Birkhauser Verlag, 95-110.

[41] A.L. Piatnitski, H.Z. Zhao and W.A. Zheng, Solutions to a class of multidimensional SPDEs, Intern. Math. Journal, Vol. 3 (2003), 755-774.

[40] A. Truman and H.Z. Zhao, Burgers equation and the WKB-Langer Asymptotic $L^{2}$ approximation of eigenfunctions and their derivatives, In: Probabilistic Methods in Fluids, World Scientific Press, Singapore, 2003, pp 332--366.

[39] I. M. Davies, A. Truman and H.Z. Zhao, Stochastic Heat and Burgers Equations and Their Singularities I--Geometrical Properties, J. Math. Phys., Vol. 43 (2002), 3293-3328.

[38] B. Oksendal, G. Vage and H.Z. Zhao, Two properties of stochastic KPP equations: ergodicity and pathwise property, Nonlinearity , Vol. 14 (2001), 639-62.

[37] B. Oksendal, G. Vage and H.Z. Zhao, Asymptotic properties of the solutions to stochastic KPP equations, Proc. R. Soc. Edinb., Vol.130A (2000), 1363-1381.

[36] A. Truman and H.Z. Zhao, Semi-classical limit of wave functions, Proc. Amer. Math. Soc., Vol. 128 (2000), 1003-1009.

[35] A. Truman and H.Z. Zhao, Stochastic Burgers' equations and their semi-classical expansions, Commun. Math. Phys., Vol. 194 (1998), 231-248.

[34] H.Z. Zhao, On gradients of approximate travelling waves for generalized KPP equations, Proc. R. Soc. Edinb., Vol. 127A (1997), No.2, 423-39.

[33] I. M. Davies, A. Truman and H.Z. Zhao, Stochastic generalized KPP equations, Proc. R. Soc. Edinb., Vol. 126A (1996), No. 5, 957-84.

[32] A. Truman and H.Z. Zhao, Quantum mechanics of charged particles in random electromagnetic fields, J. Math. Phys., Vol. 37 (1996), No.7, 3180-97.

[31] A. Truman and H.Z. Zhao, On stochastic diffusion equations and stochastic Burgers' equations, J. Math. Phys., Vol. 37 (1996), No.1, 283-307.

[30] X.M. Li and H.Z. Zhao, Gradient estimates and the smooth convergence of approximate travelling waves for reaction-diffusion equations, Nonlinearity, Vol. 9 (1996), No.2, 459-77.

[29] A. Truman and H.Z. Zhao, The stochastic Hamilton Jacobi equations, stochastic heat equations and Schr\"odinger equations, in: Stochastic Analysis and Applications edited by I.M. Davies, A. Truman and K.D. Elworthy, World Scientific, 1996, pp. 441-64.

[28] K. D. Elworthy and H.Z. Zhao, Approximate travelling waves for the generalized and stochastic KPP equations, in: Probability Theory and Mathematical Statistics: Proceedings of the Euler Institute Seminars Dedicated to the Memory of Kolmogorov edited by I.A. Ibragimov and A.Y. Zaitsev, Gordon & Breach Science Publishers, 1996, pp.141-54.

[27] W.D. Chen, H.Z. Zhao and Y.H. Yu, Delay-independent stability of nonautonomous difference-differential equations, Acta Mathematica Applicatae Sinica, 19(1996), No.2, 309-12.

[26] A. Truman and H.Z. Zhao, The stochastic Hamilton Jacobi theory and related topics, in: Stochastic Partial Differential Equations edited by A.M. Etheridge, London Mathematical Society Lecture Note Series 216, Cambridge University Press, 1995, pp. 287-303.

[25] H.Z. Zhao, The travelling wave fronts of nonlinear reaction-diffusion systems via Freidlin's stochastic approaches, Proc. R. Soc. Edinb., Vol. 124A (1994), 273-99.

[24] K. D. Elworthy and H.Z. Zhao, The propagation of traveling waves for stochastic generalized KPP equations, Mathl. and Comput. Modelling, Vol. 20 (1994), No.4/5, 131-66.

[23] K. D. Elworthy, A. Truman and H.Z. Zhao, with an Appendix by J.G. Gaines, Approximate travelling wave for the generalized KPP equations and classical mechanics, Proc. R. Soc. Lond, A (1994) 446, 529-54.

[22] H.Z. Zhao, The stability of retarded difference-differential equations with slowly varying coefficients, Acta Mathematica Applicatae Sinica, 16(1993), No.4, 493-9.

[21] H.Z. Zhao, Complex Hopf bifurcation of integral surfaces, Acta

Mathematica Applicatae Sinica, English Series, 9(1993), No.4,

348-66.  Full paper open DOI-10.1007/BF02006923

[20] H.Z. Zhao, On the structure of integral surfaces near a high

order focus and saddle, Acta Mathematica Applicatae Sinica, English

Series, 9(1993), No.2, 155-65. Full paper open DOI -10.1007/BF02007439

[19] H.Z. Zhao and K. D. Elworthy, The travelling wave solutions of

scalar generalized KPP equations via classical mechanics and

stochastic approaches, in: Stochastics and Quantum Mechanics edited

by A. Truman and I.M. Davies, World Scientific, 1992, pp. 298-316.

[18] Y.X. Qin, H.Z. Zhao, The theory of singular points of ordinary

differential equations in complex domain, Acta Mathematica Applicatae

Sinica, English Series, 8(1992), No.4, 298-317. Full paper open  DOI

- 10.1007/BF02006739

[17] H.Z. Zhao and L. Wang, The stability of nonautonomous Volterra

integro-differential equations, Chinese Science Bulletin, 37(1992),

1753-5.

[16] L. Wang and H.Z. Zhao, The stability of nonautonomous retarded

difference-differential equations, Acta Mathematica Sinica, New

Series, 8(1992), No.4, 349-56.

[15] H.Z. Zhao, and C.S. Zheng, The stability of nonautonomous vector

volterra integro-differential equations, Proceedings of Stability

Theory of Differential Equations, edited by L. Wang et al, Science

Press, Beijing, 1992, pp. 107-8.

[14] W.Z. Huang, H.Z. Zhao and S.S. Wang, The periodic three

solutions of multiparameter one-dimensional maps, in: Proceedings of

Ordinary Differential Equations, Beijing (1991) edited by Y.S. Chin

et al, Science Press, Beijing, 1991, pp. 382-7.

[13] H.Z. Zhao, The Hopf bifurcations of ordinary differential

equations with complex coefficients in complex domain, in:

Proceedings of Ordinary Differential Equations, Beijing (1991) edited

by Y.S. Chin et al, Science Press, Beijing, 1991, pp. 8-14.

[12] H.Z. Zhao, On the structure of integral surfaces near a high

order focus and saddle, Chinese Science Bulletin, (Chinese edition) 36

(1991), No.6, 475-476; (English edition) 36(1991), No.13, 1139-40.

[11] H.Z. Zhao, Z.S. Feng and K.Q. Qian, Delay-independent

stablization of linear control system with multiple delays, in:

Proceedings of Ordinary Differential Equations, Beijing (1991),

edited by Y.S. Chin et al, Science Press, Beijing 1991, pp. 414-9.

[10] H.Z. Zhao, The periodic solutions of Riccati equation with

periodic coefficients, Annals of Differential Equations, 7(1991), No.

4, 492-5.

[9] Z.S. Feng, Y. Q. Liu, H.Z. Zhao, Sufficient and necessary

conditions for delay independent stability of linear differential

difference equations, Applied Mathematics and Computations, 46

(1991), No.1, 23-32.

[8] H.Z. Zhao, The calculations of normal forms of some complex

systems, Journal of Beijing Institute of Technology, 10(1990), No.S2,

31-8.

[7] H.Z. Zhao, The bifurcations of integral surfaces from a high

order focus, Chinese Science Bulletin, (Chinese edition) 35(1990), No.

14, 1114-5; (English edition) 36(1991), No.13,1137-9.

[6] H.Z. Zhao, The complex Hopf bifurcation, Chinese Science

Bulletin, (Chinese edition) 35(1990), No.13, 1034-5; (English

edition) 36(1991), No.13, 1135-36.

[5] H.Z. Zhao, The periodic solutions of Riccati equation with

periodic coefficients, Chinese Science Bulletin, (Chinese edition) 35

(1990), No.4, 314-5; (English edition) 35(1990), No.23, 2018-20.

[4] H.Z. Zhao, The Smale horseshoe in H\'enon map, Chinese Science

Bulletin, 34(1989), No.11, 875.

[3] H.Z. Zhao, The asymptotic behaviour of ordinary differential

equations, Chinese Quarterly Journal of Mathematics, 3(1988), No.3,

43-51.

[2] H.Z. Zhao, The global asymptotic stability of second order

nonlinear differential equations, Journal of Beijing Institute of

Technology, 7(1987), No.4, 72-83.

[1] H.Z. Zhao, The stability of systems with separate variables and

slowly varying coefficients, Acta Mathematica Applicatae Sinica, 11

(1988), No.4, 478-92.