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Stochastic functional Hamiltonian system with singular coefficients

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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 Holder-Dini continuous perturbation.… Click to show full 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 Holder-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: singular coefficients; stochastic functional; hamiltonian system; functional hamiltonian; system singular

Journal Title: Communications on Pure and Applied Analysis
Year Published: 2020

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