Distribution-Dependent Stochastic Differential Delay Equations in finite and infinite dimensions

Rico Heinemann

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arXiv · 2005.07446

Distribution-Dependent Stochastic Differential Delay Equations in finite and infinite dimensions

Rico Heinemann

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Abstract

We prove that distribution dependent (also called McKean--Vlasov) stochastic delay equations of the form \begin{equation*} \mathrm{d}X(t)= b(t,X_t,\mathcal{L}_{X_t})\mathrm{d}t+ \sigma(t,X_t,\mathcal{L}_{X_t})\mathrm{d}W(t) \end{equation*} have unique (strong) solutions in finite as well as infinite dimensional state spaces if the coefficients fulfill certain monotonicity assumptions.

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Rico Heinemann. 2020-05-15. Distribution-Dependent Stochastic Differential Delay Equations in finite and infinite dimensions. https://arxiv.org/abs/2005.07446

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