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

Jonas Lieber (1) , Nadia Oudjane (2) , Francesco Russo (1, 3)

1 UMA - Unité de Mathématiques Appliquées
2 FiME Lab - Laboratoire de Finance des Marchés d'Energie
3 OC - Optimisation et commande

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).

Keywords: McKean Stochastic Differental Equations; Semilinear Partial Differential Equations; McKean Feynman-Kac equation; Probabilistic representation of PDEs; and phrases McKean Stochastic Differental Equations; Semilinear Partial Dif- ferential Equations; Probabilistic representation of PDEs 2010 AMS-classification: 60H10

Domains: Mathematics [math]; Probability [math.PR]

Jonas Lieber, Nadia Oudjane, Francesco Russo. On the well-posedness of a class of McKean Feynman-Kac equations. Markov Processes And Related Fields, 2017, 25 (5), pp.821-862. ⟨hal-01895210v2⟩