Department of Mathematics and Statistics
University of Jyväskylä
31th Jyväskylä Summer School

Course MA3:

Stochastic Modelling and Numerical Tools around the Physics of Complex Flows
Mireille Bossy (Centre Inria Sophia Antipolis- Méditerranée, France)

Abstract

The main objective of these lectures is to give a concise overview of the theory of stochastic differential equations (SDE), as modelling and numerical tools. Starting form the basic properties of SDEs, the lectures will present different aspects of the theory, motivated and illustrated by their use in turbulent transport and its simulation. Stochastic differential equation are used in physics of fluids and in many related engineering approaches for industrial and environmental applications. SDEs' theory and turbulent transport have a long common history. Yet the design of predictive simulation tools for pollutant dispersion, sedimentation in the ocean, or many energy production processes, greatly challenge researches in the field of SDEs and their simulation, combining together all the aspects presented in this course. Prerequisites: Standard measure, integration, and probability theory. Brownian motion, Itô's formula, continuous time martingales, and Markov processes.

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