Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients

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

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...

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...

Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients

We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients. Following this concept, we discard the approximate trajectories which leave a sufficiently large sphere. We prove that accuracy of any method of weak order p is estimated by ε + O(hp), where ε can ...

Asymptotic Solutions of Semilinear Stochastic Wave Equations

Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponenti...