Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes

摘要: Stochastic models that account for sudden, unforeseeable events play a crucial role in many different fields such as finance, economics, biology, chemistry, physics and so on. That kind of stochastic problems can be modeled by differential equations driven jump-diffusion processes. In addition, there are situations, where model is based on with multiple scales. Such called stiff lead classical explicit integrators the Euler-Maruyama method to time stepsize restrictions due stability issues. This opens door stabilized numerical methods efficiently tackle situations. this thesis we introduce first multilevel Monte Carlo equations. Using S-ROCK show approach very efficient scales, but also nonstiff significant noise part. Further, present an improved version considering higher weak order convergence. Then extend We study detail strong convergence newly introduced discuss corresponding mean square domains. next part state prove theorem indicates computational cost required achieve certain accuracy. section compare two variance reduction techniques, antithetic control variates. how processes, thesis, used create jump-diffusions handles stiffness considers inclusion jumps at same time. Finally, propose variable stepping algorithm uses approximate solutions A rigorous analytical carried out derive computable leading term discretization error adaptive suggested adapts grid adjusts number stages simultaneously.