Mean Square Finite-Approximate Controllability of Semilinear Stochastic Differential Equations with Non-Lipschitz Coefficients

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 ...

Approximate Boundary Controllability for Semilinear Delay Differential Equations

Controllability of Stochastic Semilinear Functional Differential Equations in Hilbert Spaces

In this paper approximate and exact controllability for semilinear stochastic functional differential equations in Hilbert spaces is studied. Sufficient conditions are established for each of these types of controllability. The results are obtained by using the Banach fixed point theorem. Applications to stochastic heat equation are given.

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...

A Class of Degenerate Stochastic Differential Equations with Non-lipschitz Coefficients

We obtain sufficient condition for SDEs to evolve in the positive orthrant. We use comparison theorem arguments to achieve this. As a result we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs with non-Lipschitz diffusion coefficients.