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