This course gives an introduction to the theory of stochastic differential equations (SDEs), explains real-life applications, and introduces numerical methods to solve these equations. Stochastic differential equation models play a prominent role in a range of application areas, including biology, chemistry, epidemiology, mechanics, microelectronics, economics, and finance. With the ongoing development of powerful computers, there is a real need to solve these stochastic models. The corresponding SDEs generalise the ordinary deterministic differential equations (ODEs).
Similarly to (deterministic) ODEs, analytical solutions of SDEs are rare, and therefore, numerical approximations have to be developed.
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