Calculus, including integration, differentiation, and differential equations are of fundamental importance for modelling in most branches on natural sciences. However, these tools are insufficient to model phenomena which include ”chance” or ”uncertainty”, like noise disturbances of signals in engineering, uncertainty about future stock prices in finance, and the macroscopic result of many microscopic particle movements in natural sciences. Among the most important tools required for the modelling of the latter phenomena are stochastic analysis and stochastic differential equations. The course gives a solid basic knowledge of stochastic analysis and stochastic differential equations. Tools from calculus, probability theory and stochastic processes that are required in stochastic calculus. Brownian motion calculus. Elements of Levy processes and martingales. Stochastic integrals. Stochastic differential equations. Examples of applications in engineering, mathematical finance and natural sciences. Numerical methods for stochastic differential equations.
- första halvan av hösten
- tillsammans med Chalmers TMS165