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Time reversal of finite and infinite dimensional diffusion processes

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  • UserAnnie Millet (Université Paris 1)
  • ClockTuesday 16 July 2024, 11:00-12:00
  • HouseExternal.

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DMLW01 - International workshop on diffusions in machine learning: foundations, generative models, and optimisation

We study finite dimensional diffusion processes (Xt, t ∈ [0, 1]) such that Xt has a density for every t > 0. We give a necessary and sufficient condition for the time reversed process (Yt = X1−t, t ∈ [0, 1]) to be a diffusion, and identify its diffusion and drift coefficients. We prove similar results for a diffusion (Xit, i ∈ Z, t ∈ [0, 1]) solution to an infinite dimensional system of SDEs. The proofs use stochastic calculus of variations; this is joint work with D. Nualart and M. Sanz-Sol´e.

This talk is part of the Isaac Newton Institute Seminar Series series.

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Kirby Laing Centre The BioPark, Hertfordshire, AL78 3AX, UK TBC, Computer Laboratory

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