On the Well-Posedness of a Class of McKean Feynman\tire Kac Equations
J. Lieber, N. Oudjane, F. Russo
2019, v.25, Issue 5, 821-862
ABSTRACT
We analyze the well-posedness of a so called McKean
Feynman\tire Kac Equation (MFKE), which is a McKean type equation with
a Feynman\tire 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\tire Kac equation; probabilistic representation of PDEs
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