Gerencser, M. (2023, October 18). Regularisation by noise in stochastic analysis [Presentation]. Mathematisches Kolloquium Universität Wien 2023, Wien, Austria.
Regularisation by noise; stochastic differential equations
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Abstract:
Introducing randomness to a deterministic problem is a common principle throughout mathematics, often leading to surprising new insights. This effect is particularly pronounced in the context of differential equations, where it has been long observed that the addition of noise in the dynamics, can in many cases dramatically improve certain properties of the system. This improvement can manifest in restoring existence or uniqueness of solutions, or even giving a meaning to an a priori ill-defined equation. In this talk we overview the history, the recent progress, and the outlook of this "regularisation by noise" phenomena.
