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

Jonas Lieber, Nadia Oudjane and Francesco Russo
october, 2019
Publication type:
Paper in peer-reviewed journals
Markov Processes and Related Fields., vol. 25, pp. 821-862
assets/images/icons/icon_arxiv.png 1810.10205
Keywords :
McKean Stochastic Differental Equations; Semilinear Partial Differential Equations; McKean Feynman-Kac equation; Probabilistic representation of PDEs.
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).
    author={Jonas Lieber and Nadia Oudjane and Francesco Russo },
    title={On the well-posedness of a class of McKean Feynman-Kac 
           equations },
    journal={Markov Processes and Related Fields. },
    year={2019 },
    volume={25 },