Exact Solvability of Stochastic Differential Equations Driven by Finite Activity Levy Processes

The Euler Scheme for Levy Driven Stochastic Differential Equations∗

In relation with Monte-Carlo methods to solve some integro-differential equations, we study the approximation problem of IEg(XT ) by IEg(X̄n T ), where (Xt, 0 ≤ t ≤ T ) is the solution of a stochastic differential equation governed by a Lévy process (Zt), (X̄n t ) is defined by the Euler discretization scheme with step Tn . With appropriate assumptions on g(·), we show that the error IEg(XT ) − I...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Backward Doubly Stochastic Differential Equations Driven by Levy Process : The Case of Non-Liphschitz Coefficients

In this work we deal with a Backward doubly stochastic differential equation (BDSDE) associated to a random Poisson measure. We establish existence and uniqueness of the solution in the case of non-Lipschitz coefficients.

Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian

Time Reversal of Volterra Processes Driven Stochastic Differential Equations

We consider stochastic differential equations driven by some Volterra processes. Under time reversal, these equations are transformed into past dependent stochastic differential equations driven by a standard Brownian motion. We are then in position to derive existence and uniqueness of solutions of the Volterra driven SDE considered at the beginning.