Distances between transition probabilities of diffusions and applications to nonlinear Fokker–Planck–Kolmogorov equations

By Vladimir Bogachev, Michael Röckner, S. Shaposhnikov. 2016

61 citations recorded by the source corpus.

Subfields: Finance, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4c0c11679f0802e24a359fb791e5ea3577306f8f

Citations in the corpus

• McKean–Vlasov SDEs under measure dependent Lyapunov conditions (2018, unknown): “The law of such an SDE satisfies a nonlinear Fokker–Planck–Kolmogorov equation (see also [4] and more generally [3]): writing μt := L (xt) and a := 12σσ ∗ we have, for t ∈ I, 〈μt, φ〉 = 〈μ0, φ〉+ ∫ t 0 〈 μs, b(s, ·, μs)∂xφ+ tr ( a(s, ·, μs)∂(2) xφ )〉 ds ∀φ ∈ C(2) 0 (D) .”