Nonlinear Diffusions and StableLike Processes wit

Authors: Vassili N Kolokoltsov

Publish Date: 2013/03/27

Volume: 68, Issue: 1, Pages: 85-98

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Abstract

The paper is devoted to the wellposedness for nonlinear McKeanVlasov type diffusions with coefficients depending on the median or more generally on the αquantile of the underlying distribution The median is not a continuous function on the space of probability measures equipped with the weak convergence This is one reason why wellposedness of the SDE considered in the paper does not follow by standard argumentsIn June 2012 on a conference in Bielefeld after the author made the presentation of his theory of nonlinear Markov processes Tom Kurtz asked him whether his methods would allow to get wellposedness for nonlinear McKeanVlasov type diffusions with coefficients depending on the distribution via the median The present paper is the answer to this question The author is also grateful to Yu Kondratiev and L Bogachev for organizing this stimulating conference in Bielefeld to Sigurd Assing and Astrid Hilbert for fruitful discussion and to the unknown referees for useful comments Supported by the AFOSR grant FA95500910664 by IPI RAN grants RFBR 110112026 and 120700115 and by the grant 4402 of the Ministry of Education and Science of Russia

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