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Applied stochastic differential equations

Technical systems and processes are often based on deterministic behavior. But a multitude of human users also causes random behavior in such systems. The load profile of a company that provides electricity, a server or the transport of goods, come about through such interactions.

With stochastic differential equations we describe both constituents of such models. We describe the deterministic behavior with the drift and the random behavior with the diffusion coefficient. With computers and mathematical software available today, we can simulate a reasonable number of trajectories in a reasonable time. A statistical analysis then provides a basis for decision-making in process planning. In an Innosuisse (formely CTI) project, we implement our ideas with an industrial partner.