ABSTRACT
This chapter discusses the problem of introducing stochasticity in mathematical modelling of dynamical systems by means of the Wiener process. Stochastic differential equations entail the best of two worlds, i.e., a combination of physical knowledge (laws of motion, preservation of energy etc.) that may be used to develop a deterministic model of the system and statistical methods for parameter estimation and model validation. The chapter briefly considers adding stochasticity to dynamical systems and informally introduces stochastic calculus while considering stochastic integrals. It presents concepts from stochastic processes and probability theory, and formally introduces Ito stochastic calculus. The chapter also provides a brief overview of jump processes and related mathematical tools.
