Mild Solutions of Neutral Semilinear Stochastic Functional Dynamic Systems with Local Non-Lipschitz Coefficients

Existence and Uniqueness of Mild Solutions to Some Neutral Stochastic Partial Functional Integrodifferential Equations with Non-Lipschitz Coefficients

Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients

The numerical methods in the current known literature require the stochastic differential equations SDEs driven by Poisson randommeasure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler’s method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. Themain aim...

On Stochastic Evolution Equations with Non-lipschitz Coefficients

In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that is, backward stochastic evolution equations, stochastic Volterra type evolution equations and stochastic functional evolution equations. In particular, the results can be used to treat a large class of quasi-linear stochastic equations, wh...

Existence-uniqueness for Stochastic Functional Differential Equations with Non-Lipschitz Coefficients

The main aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs) with non-Lipschitz coefficients. Firstly, we show that Peano’s theorem holds for SFDEs, that is, the continuity alone is sufficient to prove the local existence of the initial value problem of SFDEs. Secondly, some new uniqueness theorems are established by the comparison methods...