A Class of degenerate Stochastic differential equations with non-Lipschitz coefficients

TL;DR

This paper establishes conditions under which certain multidimensional degenerate stochastic differential equations with non-Lipschitz coefficients have unique strong solutions, ensuring their solutions remain in the positive orthant.

Contribution

It provides new sufficient conditions for the existence and uniqueness of solutions for a class of degenerate SDEs with non-Lipschitz diffusion coefficients.

Findings

Solutions remain in the positive orthant under given conditions

Existence of unique strong solutions for the class of SDEs

Comparison theorem used to establish results

Abstract

We obtain sufficient condition for SDEs to evolve in the positive orthant. We use comparison theorem arguments to achieve this. As a result we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs with non-Lipschitz diffusion coefficients.