Large deviation properties of weakly interacting processes via weak convergence methods

By A. Budhiraja, Paul Dupuis, Markus Fischer. 2010

125 citations recorded by the source corpus.

We study large deviation properties of systems of weakly interacting particles modeled by Ito stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures converges, as the number of particles tends to infinity, to the weak solution of an associated McKean–Vlasov equation. We derive a large deviation principle via the weak convergence approach. The proof, which avoids discretization arguments, is based on a representation theorem, weak convergence and ideas from stochastic optimal control. The method works under rather mild assumptions and also for models described by SDEs not of diffusion type. To illustrate this, we treat the case of SDEs with delay.

Subfields: Applied Mathematics, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/545c7771cd272b98536d1f262b2e2ba6d98e22cc

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In Applied Mathematics

In Finance

In Statistical and Nonlinear Physics

Citations in the corpus

From the master equation to mean field game limit theory: Large deviations and concentration of measure (2018, methodology): “Our proof relies on the so-called contraction principle, which is somewhat similar to the approach developed in [9] and [22].”