On near-martingales and a class of anticipating linear SDEs
Probability
2022-04-06 v1
Abstract
The primary goal of this paper is to prove a near-martingale optional stopping theorem and establish solvability and large deviations for a class of anticipating linear stochastic differential equations. We prove the existence and uniqueness of solutions using two approaches: (1) Ayed-Kuo differential formula using an ansatz, and (2) a novel braiding technique by interpreting the integral in the Skorokhod sense. We establish a Freidlin-Wentzell type large deviations result for solution of such equations.
Keywords
Cite
@article{arxiv.2204.01932,
title = {On near-martingales and a class of anticipating linear SDEs},
author = {Hui-Hsiung Kuo and Pujan Shrestha and Sudip Sinha and Padmanabhan Sundar},
journal= {arXiv preprint arXiv:2204.01932},
year = {2022}
}
Comments
23 pages, 2 figures