Stochastic functional Hamiltonian system with singular coefficients

Xing Huang; Wujun Lv

doi:10.3934/cpaa.2020060

Article Contents

2020, Volume 19, Issue 3: 1257-1273. Doi: 10.3934/cpaa.2020060

This issue Previous Article Hydrodynamic limit of the kinetic thermomechanical Cucker-Smale model in a strong local alignment regime Next Article Convergence of lacunary SU(1, 1)-valued trigonometric products

Stochastic functional Hamiltonian system with singular coefficients

Xing Huang^1, , and
Wujun Lv^2,

1.
Center for Applied Mathematics, Tianjin University, Tianjin 300072, China
2.
Department of Statistics, College of Science, Donghua University, Shanghai 201620, China

^* Corresponding author
^* Corresponding author

Received: January 31, 2019

Revised: July 31, 2019

Published: February 2020

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Abstract

By Zvonkin type transforms, the existence and uniqueness of the strong solutions for a class of stochastic functional Hamiltonian systems are obtained, where the drift contains a Hölder-Dini continuous perturbation. Moreover, under some reasonable conditions, the non-explosion of the solution is proved. In addition, as applications, the Harnack and shift Harnack inequalities are derived by method of coupling by change of measure. These inequalities are new even in the case without delay and the shift Harnack inequality is also new even in the non-degenerate functional SDEs with singular drifts.

Keywords:

Hölder-Dini continuous,
stochastic functional Hamiltonian system,
Zvonkin type transform,
functional SDEs,
Harnack inequalities.

Mathematics Subject Classification: Primary: 60H10, 60H15.

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