McKean-Vlasov limit for interacting random processes in random media
P. Dai Pra,W.T.F. den Hollander +1 more
TLDR
In this paper, the authors apply large deviation theory to particle systems with a random mean-field interaction in the McKean-Vlasov limit and describe large deviations and normal fluctuations around the MCV equation.Abstract:
We apply large-deviation theory to particle systems with a random mean-field interaction in the McKean-Vlasov limit. In particular, we describe large deviations and normal fluctuations around the McKean-Vlasov equation. Due to the randomness in the interaction, the McKean-Vlasov equation is a collection of coupled PDEs indexed by the state space of the single components in the medium. As a result, the study of its solution and of the finite-size fluctuation around this solution requires some new ingredient as compared to existing techniques for nonrandom interaction.read more
Citations
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Mean-Field Backward Stochastic Differential Equations and Related Partial Differential Equations ∗
TL;DR: In this paper, a mean-field backward stochastic differential equation (SDE) is studied in a Markovian framework, associated with a McKean-Vlasov forward equation.
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Metastability in stochastic dynamics of disordered mean-field models
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Mean-field stochastic differential equations and associated PDEs
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References
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Book
Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
Book
Markov Processes: Characterization and Convergence
TL;DR: In this paper, the authors present a flowchart of generator and Markov Processes, and show that the flowchart can be viewed as a branching process of a generator.
Book
Statistics of random processes
TL;DR: In this paper, the optimal linear non-stationary filtering, interpolation and extrapolation of Partially Observable Random Processes with a Countable Number of States (POMOS) was studied.