Invariant measures related with Poisson driven stochastic differential equation

Invariant measures for Burgers equation with stochastic forcing

Finite Element Approximation of Stochastic Partial Differential Equations driven by Poisson Random Measures of Jump Type

where f : R×O → R and g : R×R → R are global Lipschitz continuous functions and η is a space time Poisson random measure of impulsive type (see, e.g., Saint Loubert Bié [SLB98] or Peszat and Zabczyk [PZ07]). Non-Gaussian random processes play an increasing rôle in modeling stochastic dynamical systems. Typical examples of non-Gaussian stochastic processes are Lévy processes and processes arisin...

Invariant measures for a stochastic Kuramoto-Sivashinky equation

For the 1-dimensional Kuramoto–Sivashinsky equation with random forcing term, existence and uniqueness of solutions is proved. Then, the Markovian semigroup is well defined; its properties are analyzed, in order to provide sufficient conditions for existence and uniqueness of invariant measures for this stochastic equation. Finally, regularity results are obtained by means of Girsanov theorem.

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

An Euler-Poisson scheme for Lévy driven stochastic differential equations

We describe an Euler scheme to approximate solutions of Lévy driven stochastic differential equations (SDEs) where the grid points are given by the arrival times of a Poisson process and thus are random. This result extends the previous work of FerreiroCastilla et al. (2014). We provide a complete numerical analysis of the algorithm to approximate the terminal value of the SDE and prove that th...