# Reflected backward doubly stochastic differential equations with time delayed generators

## TL;DR

This paper studies a class of reflected backward doubly stochastic differential equations with generators depending on past solution values, establishing existence and uniqueness under Lipschitz conditions.

## Contribution

It introduces and analyzes RBDSDEs with time-delayed generators, extending the theory to include dependence on past solutions.

## Key findings

- Existence and uniqueness of solutions under Lipschitz conditions.
- Extension of RBDSDE theory to time-delayed generators.
- Framework for future applications in stochastic control and finance.

## Abstract

We consider a class of reflected backward doubly stochastic differential equations with time delayed generator (in short RBDSDE with time delayed generator), in this case generator at time $t$ can depend on the values of a solution in the past. Under a Lipschitz condition, we ensure the existence and uniqueness of the solution.