论文标题
有限和无限尺寸中的分布依赖性随机差延迟方程
Distribution-Dependent Stochastic Differential Delay Equations in finite and infinite dimensions
论文作者
论文摘要
我们证明了表格\ begin {equation*} \ mathrm {d} x（t）= b（t，x_t，x_t，\ mathcal {l} _ {x_t} _ {x_t}） σ（t，x_t，\ Mathcal {l} _ {x_t}）\ Mathrm {d} w（t）W（t）\ end {equication*}，如果系数满足某些单调性假设，则在有限的dimenite dimemential状态空间中具有独特的（强）溶液。
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+ σ(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.
