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Title: Nonlinear Diffusions and Stable-Like Processes with Coefficients Depending on the Median or VaR

The paper is devoted to the well-posedness for nonlinear McKean-Vlasov type diffusions with coefficients depending on the median or, more generally, on the {alpha}-quantile 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 well-posedness of the SDE considered in the paper does not follow by standard arguments.
Authors:
 [1]
  1. University of Warwick, Department of Statistics (United Kingdom)
Publication Date:
OSTI Identifier:
22122869
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 68; Journal Issue: 1; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; DIFFUSION; FUNCTIONS; NONLINEAR PROBLEMS; PROBABILITY; SPACE DEPENDENCE