Existence and uniqueness of solutions for stochastic differential equations with locally one-sided Lipschitz condition

Abstract

This paper investigated stochastic differential equations (SDEs) with locally one-sided Lipschitz coefficients. Apart from the local one-sided Lipschitz condition, a more general condition was introduced to replace the monotone condition. Then, in terms of Euler's polygonal line method, the existence and uniqueness of solutions for SDEs was established. In the meanwhile, the $ p $th moment boundedness of solutions was also provided.

Keywords

• stochastic differential equations
• locally one-sided lipschitz
• existence and uniqueness
• moment boundedness