Distribution dependent SDEs with singular coefficients

By Xing Huang, Feng-Yu Wang. Stochastic Processes and their Applications, 2018

169 citations recorded by the source corpus.

Under integrability conditions on distribution dependent coefficients, existence and uniqueness are proved for McKean-Vlasov type SDEs with non-degenerate noise. When the coefficients are Dini continuous in the space variable, gradient estimates and Harnack type inequalities are derived. These generalize the corresponding results derived for classical SDEs, and are new in the distribution dependent setting.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/bdcf10c4c89c0190a3354e19db4a5d8968f1cac3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Finance

Citations in the corpus

Distribution dependent SDEs driven by additive fractional Brownian motion (2021, methodology): “Let us stress that, since we are not allowed to use the same tools as in the Brownian setting, our results are not optimal for the choice H = 1/2, sharper ones being available for instance in [25, 40].”
Distribution dependent SDEs driven by fractional Brownian motions (2021, background): “mention, for examples, the works in [10, 11, 18] for large scale social interactions within the memory of mean-field games, [8, 13, 23] for value functions and related PDEs, [19, 20, 32, 36] for (shift) Harnack type inequalities and gradient estimates, and the references therein.”
Mckean-Vlasov sdes with drifts discontinuous under wasserstein distance (2020, methodology): “Recently, the (weak and strong) well-posedness is studied in [3, 4, 6, 13, 17, 18, 20] for (1) with σt(x, γ) = σt(x) independent of the distribution variable γ, and with singular drift bt(x, γ).”