Stochastic Modeling and Simulation of Microscopic Processes

Abstract: In this thesis we study analytical and numerical methods which describe interactions and evolution of complex physical systems modeled by microscopic processes. We focus on two types of systems which are differentiated based on how modeling is taking place at the microscopic level. In that respect we study systems which can be described either by stochastic differential equations or by elementary microscopic stochastic processes. For the case of stochastic differential equations, we illustrate how to produce their solutions both analytically and numerically. For the case of elementary microscopic stochastic processes it is unrealistic to expect that an analytic solution would always exist since often such systems can be transient and out of equilibrium. We therefore produce numerical solutions for those systems which are based on Monte Carlo simulations. We constitute the respective analytic solutions and numerical methods from two vastly different research areas such as finance and traffic flow in order to better illustrate the wide applicability of such methods