On the Wellposedness of Some McKean Models with Moderated or Singular Diffusion Coefficient

J. M. Jabir; Bossy M.

doi:10.1007/978-3-030-22285-7_2

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On the Wellposedness of Some McKean Models with Moderated or Singular Diffusion Coefficient

Ch. 2. P. 43–87.

Jabir J. M., Bossy M.

We investigate the well-posedness problem related to two models of nonlinear McKean Stochastic Differential Equations with some local interaction in the diffusion term. First, we revisit the case of the McKean-Vlasov dynamics with moderate interaction, previously studied by Méléard and Jourdain in [16], under slightly weaker assumptions, by showing the existence and uniqueness of a weak solution using a Sobolev regularity framework instead of a Hölder one. Second, we study the construction of a Lagrangian Stochastic model endowed with a conditional McKean diffusion term in the velocity dynamics and a nondegenerate diffusion term in the position dynamics.

Language: English

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Keywords: Weak-strong wellposedness problems McKean-Vlasov models Singular McKean diffusions

In book

Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications, Edinburgh, July 2017. Selected, Revised and Extended Contributions

Springer, 2019.

Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications, Edinburgh, July 2017. Selected, Revised and Extended Contributions

Springer, 2019.

This collection of selected, revised and extended contributions resulted from a Workshop on BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and included the 8th World Symposium on BSDEs. The volume addresses recent advances involving backward stochastic differential equations (BSDEs) and stochastic partial differential equations (SPDEs). These equations are of fundamental ...

Added: September 24, 2020