NDLI: Nonequilibrium Markov Processes Conditioned on Large Deviations

Content Provider	Springer Nature Link
Author	Chetrite, Raphaël Touchette, Hugo
Copyright Year	2014
Abstract	We consider the problem of conditioning a Markov process on a rare event and of representing this conditioned process by a conditioning-free process, called the effective or driven process. The basic assumption is that the rare event used in the conditioning is a large deviation-type event, characterized by a convex rate function. Under this assumption, we construct the driven process via a generalization of Doob’s h-transform, used in the context of bridge processes, and show that this process is equivalent to the conditioned process in the long-time limit. The notion of equivalence that we consider is based on the logarithmic equivalence of path measures and implies that the two processes have the same typical states. In constructing the driven process, we also prove equivalence with the so-called exponential tilting of the Markov process, often used with importance sampling to simulate rare events and giving rise, from the point of view of statistical mechanics, to a nonequilibrium version of the canonical ensemble. Other links between our results and the topics of bridge processes, quasi-stationary distributions, stochastic control, and conditional limit theorems are mentioned.
Starting Page	2005
Ending Page	2057
Page Count	53
File Format	PDF
ISSN	14240637
Journal	Annales Henri Poincaré
Volume Number	16
Issue Number	9
e-ISSN	14240661
Language	English
Publisher	Springer Basel
Publisher Date	2014-10-12
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Dynamical Systems and Ergodic Theory Quantum Physics Mathematical Methods in Physics Classical and Quantum Gravitation, Relativity Theory Elementary Particles, Quantum Field Theory
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Nuclear and High Energy Physics Mathematical Physics

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