Numerical Simulations of Linear Stochastic Oscillators : driven by Wiener and Poisson processes

Abstract: The main component of this essay is the numerical analysis of stochastic differential equations driven by Wiener and Poisson processes. In order to do this, we focus on two model problems, the geometric Brownian motion and the linear stochastic oscillator, studied in the literature for stochastic differential equations only driven by a Wiener process. This essay covers theoretical as well as numerical investigations of jump - or more specifically, Poisson - processes and how they influence the above model problems.