Large rank-based models with common noise

Publication date: Available online 22 March 2019Source: Statistics & Probability LettersAuthor(s): Praveen Kolli, Andrey SarantsevAbstractFor large systems of Brownian particles interacting through their ranks introduced in (Banner et al., 2005), the empirical cumulative distribution function satisfies a porous medium PDE. However, when we introduce a common noise, the limit is no longer deterministic. Instead, we show that this limit is a solution of a stochastic PDE related to this porous medium PDE. This stochastic PDE is somewhat similar to the equations developed for conservation laws with rough stochastic fluxes (Lions et al., 2013).

Source: Statistics and Probability Letters - March 22, 2019 Category: Statistics Source Type: research