Existence of Affine Realizations for Stochastic Partial Differential Equations Driven by Lévy Processes

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

Covariance Structure of Parabolic Stochastic Partial Differential Equations with Multiplicative Lévy Noise

We consider parabolic stochastic partial differential equations driven by multiplicative Lévy noise of an affine type. For the second moment of the mild solution, we derive a well-posed deterministic space-time variational problem posed on tensor product spaces, which subsequently leads to a deterministic equation for the covariance function.

Reflected generalized backward doubly SDEs driven by Lévy processes and Applications

In this paper, a class of reflected generalized backward doubly stochastic differential equations (reflected GBDSDEs in short) driven by Teugels martingales associated with Lévy process and the integral with respect to an adapted continuous increasing process is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to ...

Existence of Affine Realizations for Lévy Term Structure Models

We investigate the existence of affine realizations for term structure models driven by Lévy processes. It turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps. As special cases, we study constant direction volatilities and the existence of short rate realizations.

Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes

Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...