Abstract. Many real processes can be modeled by stochastic differential equations with aftereffect [1]-[3]. Stability conditions for such systems can be obtained by construction of appropriate Lyapunov functionals using special procedure of Lyapunov functionals construction [4]-[14]. In this paper asymptotic mean square stability of stochastic linear differential equations with discrete and dis...

This paper is a survey of uniqueness results for stochastic differential equations with jumps and regularity results for the corresponding harmonic functions. Subject classifications: Primary 60H10; Secondary 60H30, 60J75

In [1] and [2], we studied the problem of the existence and uniqueness of a solution to some general BSDE on manifolds. In these two articles, we assumed some Lipschitz conditions on the drift f(b, x, z). The purpose of this article is to extend the existence and uniqueness results under weaker assumptions, in particular a monotonicity condition in the variable x. This extends well-known result...