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Journal Articles Markov Processes And Related Fields Year : 2019

On the well-posedness of a class of McKean Feynman-Kac equations

Abstract

We analyze the well-posedness of a so called McKean Feynman-Kac Equation (MFKE), which is a McKean type equation with a Feynman-Kac perturbation. We provide in particular weak and strong existence conditions as well as pathwise uniqueness conditions without strong regularity assumptions on the coefficients. One major tool to establish this result is a representation theorem relating the solutions of MFKE to the solutions of a nonconservative semilinear parabolic Partial Differential Equation (PDE).
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Dates and versions

hal-01895210 , version 1 (22-10-2018)
hal-01895210 , version 2 (10-10-2019)
hal-01895210 , version 3 (06-03-2024)

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Jonas Lieber, Nadia Oudjane, Francesco Russo. On the well-posedness of a class of McKean Feynman-Kac equations. Markov Processes And Related Fields, 2019, 25 (5), pp.821-862. ⟨hal-01895210v3⟩
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