Distribution-Dependent Stochastic Differential Delay Equations in finite and infinite dimensions
Probability
2020-05-18 v1
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.
Keywords
Cite
@article{arxiv.2005.07446,
title = {Distribution-Dependent Stochastic Differential Delay Equations in finite and infinite dimensions},
author = {Rico Heinemann},
journal= {arXiv preprint arXiv:2005.07446},
year = {2020}
}
Comments
30 pages