Approximate Controllability of Second-Order Stochastic Differential Systems Driven by a Lévy Process

Abstract

This paper addresses approximate controllability for a class of control systems represented by second order stochastic differential equations driven by Teugels martingales associated with a Levy process. The main technique is the fundamental solution theory constructed through Laplace transformation. By using the so-called resolvent condition and cosine family of linear operators, stochastic analysis, and the technique of stochastic control theory, a new set of sufficient conditions for the approximate controllability of the considered second order stochastic differential system are formulated and proved. Due to the fundamental solution theory, the nonlinear terms are only required to be partly uniformly bounded. As an illustration of the applications of the obtained results, an example is also provided in the end.