Non-linear stochastic diffusion processes - a guided tour into the vast world of non-Gaussian applications (Max-Olivier Hongler, EPF Lausanne)

17.05.2022 14:00

Applied mathematical modelling heavily relies on diffusion processes - i.e solutions of stochastic differential equations (SDE) driven by White Gaussian sources. In this context, the wealthiness of SDE’s applications strongly contrasts with the scarceness of analytical soluble models. Basically, besides the Ornstein-Uhlenbeck process (linear drifted SDE), other simple solvable illustrations with relevance for applications are rare - escaping the Gaussian world is definitely not an easy analytical task ! In the seminar, the Doob h-transform (i.e. change of probability measures) and closely to it, the Onsager-Machlup Lagrangian formalism will be used to unveil simple non-Gaussian tractable processes relevant for physics (diffusion over potential barriers and in potential wells) and for economy (dynamic version of the J. E. Stiglitz mean preserving spread and “honey-moon" effect for money target zones). Finally, the filtering of noisy observations of the constructed non-Gaussian processes is also fully explicit. In this case indeed, the Zakai and Kushner stochastic pde’s describing the filtering process can be solved explicitly. This naturally extends the Kalman-Bucy linear filtering to a wider class known as the Benes’s non-linear filters.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire d'analyse numérique

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