Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Research Publications


Publications for Huaizhong Zhao

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Journal Articles

Wang, Q and Zhao, H (2017) Rough path properties for local time of symmetric α stable process, Stochastic Processes and their Applications, 127(11), pp.3596-3642, ISSN: 0304-4149. DOI: 10.1016/j.spa.2017.03.006.

Feng, C, Liu, Y, Zhao, H (2017) Numerical approximation of random periodic solutions of stochastic differential equations, Zeitschrift für Angewandte Mathematik und Physik, 68(5), ISSN: 0044-2275. DOI: 10.1007/s00033-017-0868-7.

Feng, C, Wang, X, Zhao, H (2017) Quasi-linear PDEs and forward-backward stochastic differential equations: weak solutions, Journal of Differential Equations, 264(2), pp.959-1018, ISSN: 0022-0396. DOI: 10.1016/j.jde.2017.09.030.

Feng, C, Wu, Y, Zhao, H (2016) Anticipating Random Periodic Solutions--I. SDEs with Multiplicative Linear Noise, Journal of Functional Analysis, ISSN: 1096-0783. DOI: 10.1016/j.jfa.2016.04.027.

Zhang, Q and Zhao, H (2015) Backward doubly stochastic differential equations with polynomial growth coefficients, Discrete and Continuous Dynamical Systems- Series A, 35(11), pp.5285-5315, ISSN: 1078-0947. DOI: 10.3934/dcds.2015.35.5285.

Wei, L, Wu, Z, Zhao, H (2014) Sobolev weak solutions of the Hamilton Jacobi Bellman equations, SIAM Journal on Control and Optimization, 52(3), pp.1499-1526, ISSN: 0363-0129. DOI: 10.1137/120889174.

Zhang, Q and Zhao, H (2013) SPDEs with polynomial growth coefficients and the Malliavin calculus method, Stochastic Processes and their Applications, 123(6), pp.2228-2271, ISSN: 0304-4149. DOI: 10.1016/j.spa.2013.02.004.

Zhang, Q and Zhao, H (2012) Probabilistic Representation of Weak Solutions of Partial Differential Equations with Polynomial Growth Coefficients, Journal of Theoretical Probability, 25(2), pp.396-423, ISSN: 0894-9840. DOI: 10.1007/s10959-011-0350-y.

Feng, C and Zhao, H (2012) Random periodic solutions of SPDEs via integral equations and Wiener-Sobolev compact embedding, Journal of Functional Analysis, 262(10), pp.4377-4422, ISSN: 0022-1236. DOI: 10.1016/j.jfa.2012.02.024.

Yevik, A and Zhao, H (2011) Numerical approximation to the stationary solutions of stochastic differential equations, SIAM Journal on Numerical Analysis, 49, pp.1397-1416.

Feng, C, Zhao, H, Zhou, B (2011) Pathwise random periodic solutions of stochastic differential equations, Journal of Differential Equations, 251, pp.119-149.

Zhang, Q and Zhao, H (2010) Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients, Journal of Differential Equations, 248, pp.953-991.

Feng, C and Zhao, H (2010) Local time rough path for Levy processes, Electronic Journal of Probability, 15, pp.452-483.

Zhao, H and Zheng, Z (2009) Random periodic solutions of random dynamical systems, Journal of Differential Equations, 246(5), pp.2020-2038.

Yong, L and Zhao, H (2009) Representation of pathwise stationary solutions of stochastic Burgers equations, Stochastics and Dynamics, 9, pp.613-634.

Ji, S and Zhao, H (2008) On the solvability of forward-backward stochastic differential equations with absorption coefficients, Chinese Annals of Mathematics Series A, 29A(1), pp.71-82.

Feng, C and Zhao, H (2008) Rough path integral of local time, C.R. Acad. Sci. Paris, Ser. I346, pp.431-434.

Mohammad, S-E, Zhang, T, Zhao, HZ (2008) The stable manifold theorem for semilinear stochastick evolution equations and stochastic partial differential equations, Mem. Amer. Math. Soc, 196 (917), pp.1-105, ISSN: 0065-9266.

Zhao, H and Zhang, Q (2007) Stationary solutions of SPDEs and infinite horizon BDSDEs, Journal of Functional Analysis, 252(1), pp.171-219, ISSN: 0022-1236. DOI: 10.1016/j.jfa.2007.06.019.

Elworthy, KD, Truman, A, Zhao, H (2007) Generalized Ito fomulae and space-time Lebesgue-Stieltjes integrals of local times, Sèminaire de Probabilitès, 40, pp.117-136.

Feng, C and Zhao, H (2007) A Generalized Ito's Formula in Two-Dimensions and Stochastic Lebesgue-Stieltjes Integrals, Electronic Journal of Probability, 12, pp.1568-1599.

Feng, C and Zhao, H (2006) Two-parameter p,q-variation paths and integrations of local times, Potential Analysis, 25(2), pp.165-204, ISSN: 1572-929X. DOI: 10.1007/s11118-006-9024-2.

Feng, C and Zhao, H (2006) Two-parameter p,q-variation Path and Integration of Local Times, Potential Analysis, 25(2), pp.165-204.

Guo, D, Ji, S, Zhao, H (2006) On the solvability of infinite horizon forward-backward stochastic differential equations with absorption coefficients, Statistics and Probability Letters, 76, pp.1954-1960.

Davies, IM, Truman, A, Zhao, H (2005) Stochastic heat and Burgers equations and their singularities. II - analytical properties and limiting distributions, Journal of Mathematical Physics, 46, ISSN: 0022-2488. DOI: 10.1063/1.1850836.

Davies, IM, Truman, A, Zhao, H (2005) Stochastic heat and Burgers equations and their singularities. II. Analytical properties and limiting distributions, Journal of Mathematical Physics, 46(4), ISSN: 0022-2488. DOI: 10.1063/1.1850836.

Piatnitski, AL, Zhao, H, Zheng, WA (2003) Solutions to a class of Multidimensional SPDEs, International Mathematical Journal, 3, pp.755-774.

Davies, IM, Truman, A, Zhao, H (2002) Stochastic Heat and Burgers Equations and their Singularities I-Geometrical Properties, Journal of Mathematical Physics, 43, pp.3293-3328.

Oksendal, B, Vage, G, Zhao, H (2001) Two Properties of Stochastic KPP Equations: Ergodicity and Pathwise Property, Nonlinearity, 14(3), pp.639-662, ISSN: 1361-6544. DOI: 10.1088/0951-7715/14/3/311.

Øksendal, B, Våge, G, Zhao, HZ (2000) Asymptotic properties of the solutions to stochastic KPP equations, Royal Society of Edinburgh - Proceedings A, 130(6), pp.1363-1381, ISSN: 0308-2105.

Truman, A and Zhao, H (2000) Semi-Classical Limit of Wave Functions, Proceedings of the American Mathematical Society, 128, pp.1003-1009.

Oksendal, B, Vage, G, Zhao, H (2000) Asymtptotic Properties of the Solutions to Stochastic KPP Equations, Proceedings of the Royal Society of Edinburgh, 130A, pp.1363-1381, ISSN: 0308-2105. DOI: 10.1017/S030821050000072X.

Truman, A and Zhao, H (1998) Stochastic Burgers' Equations and Their Semi-Classical Expansions, Commununications in Mathematical Physics, 194, pp.231-248, ISSN: 0010-3616. DOI: 10.1007/s002200050357.

Zhao, H (1997) On Gradients of Approximate Travelling Waves for Generalized KPP Equations, Proceedings of Royal Society Edinburgh, 127A(5), pp.423-39, ISSN: 0308-2105.

Zhao, HZ (1997) On gradients of approximate travelling waves for generalised KPP equations, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 127(2), pp.423-439, ISSN: 0308-2105. DOI: 10.1017/s0308210500023738.

Li, XM and Zhao, HZ (1996) Gradient estimates and the smooth convergence of approximate travelling waves for reaction-diffusion equations, Nonlinearity, 9(2), pp.459-477, ISSN: 0951-7715. DOI: 10.1088/0951-7715/9/2/010.

Truman, A and Zhao, HZ (1996) Quantum mechanics of charged particles in random electromagnetic fields, Journal of Mathematical Physics, 37(7), pp.3180-3197, ISSN: 0022-2488. DOI: 10.1063/1.531564.

Chen, WD, Zhao, H, Yu, YH (1996) Delay-Independent Stability of Nonautonomous Difference-Differential Equations, Acta Mathematica Applicatae Sinica, 19(2), pp.309-12.

Truman, A and Zhao, H (1996) On Stochastic Diffusion Equations and Stochastic Burgers' Equations, Journal of Mathematical Physics, 37(1), pp.283-307, ISSN: 0022-2488.

Truman, A and Zhao, H (1996) Quantum Mechanics of Charged Particles in Random Electromagnetic Fields, Journal of Mathematical Physics, 37(7), pp.3180-97.

Davies, IM, Truman, A, Zhao, H (1996) Stochastic Generalized KPP Equations, Proceedings of Royal Society Edinburgh, 126A(5), pp.957-84.

Davies, IM, Truman, A, Zhao, HZ (1996) Stochastic generalised KPP equations, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 126(5), pp.957-983, ISSN: 0308-2105. DOI: 10.1017/s0308210500023192.

Truman, A and Zhao, HZ (1996) On stochastic diffusion equations and stochastic Burgers’ equations, Journal of Mathematical Physics, 37(1), pp.283-307, ISSN: 0022-2488. DOI: 10.1063/1.531391.

Elworthy, KD, Zhao, HZ, Gaines, JG (1994) The propagation of travelling waves for stochastic generalized KPP equations, Mathematical and Computer Modelling, 20(4-5), pp.131-166, ISSN: 0895-7177. DOI: 10.1016/0895-7177(94)90162-7.

Elworthy, KD, Truman, A, Zhao, H, Gaines, JG (1994) Approximate Travelling Wave for the Generalized KPP Equations and Classical Mechanics, Proceedings of Royal Society London A, 446, pp.529-54.

Zhao, H (1994) The Travelling Wave Fronts of Nonlinear Reaction-Diffusion Systems via Freidlin's Stochastic Approaches, Proceedings of Royal Society Edinburgh, 124A, pp.273-99.

Zhao, H (1993) On the Structure of Integral Surfaces Near a High Order Focus and Saddle, Acta Mathematica Applicatae Sinica, English Series, 9(2), pp.155-65.

Zhao, H (1993) Complex Hopf Bifurcation of Integral Surfaces, Acta Mathematica Applicatae Sinica, English Series, 9(4), pp.348-66.

Zhao, H (1993) The Stability of Retarded Difference-Differential Equations with Slowly Varying Coefficients, Acta Mathematica Applicatae Sinica, 16(4), pp.493-9.

Wang, L and Zhao, H (1992) The Stability of Nonautonomous Retarded Difference-Differential Equations, Acta Mathematica Sinica, 8(4), pp.349-56.

Qin, YX and Zhao, H (1992) The Theory of Singular Points of Ordinary Differential Equations in Complex Domain, Acta Mathematica Applicatae Sinica, English Series, 8(4), pp.298-317.

Zhao, H and Wang, L (1992) The Stability of Nonautonomous Volterra Integro-Differential Equations, Chinese Science Bulletin, 37, pp.1753-1755.

Liu, YQ, Feng, ZS, Zhao, H (1991) Sufficient and Necessary Conditions for Delay Independent Stability of Linear Differential Difference Equations, Journal of Applied Mathematics and Computations, 46(1), pp.23-32.

Zhao, H (1991) The Periodic Solutions of Riccati Equation with Periodic Coefficients, Annals of Differential Equations, 7(4), pp.492-5.

Zhao, H (1991) The Complex Hopf Bifurcation, Chinese Science Bulletin (Chinese Edition), 35(13), pp.1034-1035.

Zhao, H (1991) The Complex Hopf Bifurcation, Chinese Science Bulletin (English Edition), 36(13), pp.1135-1136.

Zhao, H (1991) The Bifurcations of Integral Surfaces from a High Order Focus, Chinese Science Bulletin (English Edition), 36(13), pp.1137-1139.

Zhao, H (1991) On the Structure of Integral Surfaces Near a HIgh Order Focus and Saddle, Chinese Science Bulletin (Chinese Edition), 36(6), pp.475-476.

Zhao, H (1991) On the Stucture of Integral Surfaces Near a High Order Focus and Saddle, Chinese Science Bulletin, 36(13), pp.1139-1140.

Zhao, H (1990) The Periodic Solutions of Riccati Equations with Periodic Coefficients, Chinese Science Bulletin (Chinese Edition), 35(4), pp.314-5.

Zhao, H (1990) The Periodic Solutions of Riccati Equation with Periodic Coefficients, Chinese Science Bulletin (English Edition), 35(23), pp.2018-2020.

Zhao, H (1990) The Bifurcations of Integral Surfaces from a High Order Focus, Chinese Science Bulletin (Chinese Edition), 35(14), pp.1114-1115.

Zhao, H (1990) The Calculations of Normal Forms of Some Complex Systems, Journal of Beijing Institute of Technology, 10(S2), pp.31-38.

Zhao, H (1989) The Smale Horseshoe in Henon Map, Chinese Science Bulletin, 34(11), p.875.

Zhao, H (1988) The Stability of Systems with Separate Variables and Slowly Varying Coefficients, Acta Mathematica Applicatae Sinica, 11(4), pp.478-92.

Zhao, H (1988) The Asymptotic Behaviour of Ordinary Differential Equations, Chinese Quarterly Journal of Mathematics, 3(3), pp.43-51.

Zhao, H (1987) The Global Asymptotic Stability of Second Order Nonlinear Differential Equations, Journal of Beijing Institute of Technology, 7(4), pp.72-83.



Conferences

Davies, IM, Truman, A, Zhao, H (2005) Stochastic heat and Burgers equations and their singularities. In IMA Volumes in Mathematics and its Applications, Springer, pp.75-92.

Davies, IM, Truman, A, Zhao, H (2004) Stochastic Heat and Burgers Equations and the Intermittence of Turbulence. In Birkhauser, Progress in probability, Verlag, pp.95-110.

Truman, A and Zhao, H (2003) Burgers Equation and the WKB-Langer Asymptotic L² Approximation of Eigenfunctions and their Derivatives. In Probabilistic Methods in Fluids, Singapore, pp.332-366.

Mohammed, SEA, Zhang, TS, Zhao, H (2002) Stable Manifold Theorem for Semilinear SPDE's. In International Congress of Mathematicians, Abstract of Short Communication and Poster Sessions, I. Flows and Stationary Solutions, Beijing, p.203.

Elworthy, KD and Zhao, H (1996) Approximate Travelling Waves for the Generalized and Stochastic KPP Equations. In Ibragimov, IA and Zaitsev, AYE (ed) Proceedings of the Euler Institute Seminars Dedicated to the Memory of Kolmogorov Probability Theory and Mathematical Statistics, Russia, pp.141-54.

Truman, A and Zhao, H (1996) The Stochastic Hamilton Jacobi Equations, Stochastic Heat Equations and Schr̈odinger Equations. In Davies, M, I, Truman, A, Elworthy, eds, KD (ed) Proceedings of the Conference on Stochastic Analysis and Applications, Gregnug, Wales, pp.441-64.

Truman, A and Zhao, H (1995) The Stochastic Hamilton Jacobi Theory and Related Topics. In Etheridge, AME (ed) Proceedings of the Conference on Stochastic Partial Differential Equations, Edinburgh, pp.287-303.

Zhao, H and Elworthy, KD (1992) The Travelling Wave Solutions of Scalar Generalized KPP Equations via Classical Mechanics and Stochastic Approaches. In Truman, A and Davies, IME (ed) Proceedings of the Conference on Stochastics and Quantum Mechanics, Swansea, pp.298-316.

Zhao, H and Zheng, CS (1992) The Stability of Nonautonomous Vector Volterra Integro-Differential Equations. In Editors, LWEA (ed) Proceedings of Stability Theory of Differential Equations, Beijing, pp.107-108.

Zhao, H, Feng, ZS, Qian, KQ (1991) Delay-Independent Stabilization of Linear Control System with Multiple Delays. In Editors, YSCEA (ed) Proceedings of Ordinary Differential Equations, Beijing, pp.414-419.

Zhao, H (1991) The Hopf Bifurcations of Ordinary Differential Equations with Complex Coefficients in Complex Domain. In Editors, YSCEA (ed) Proceedings of Ordinary Differential Equations, Beijing, pp.8-14.

Huang, WZ, Zhao, H, Wang, SS (1991) The Periodic Three Solutions of Multiparameter One-Dimensional Maps. In Editors, YSCEA (ed) Proceedings of Ordinary Differential Equations, Beijing, pp.382-287.



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