Work

Diffusions conditioned on occupation measures

Year: 2016

Type: article

Abstract: A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned on the fluctuation observed. We construct here this driven process for diffusions spending an atypical fraction of their evolution in some region of state space, corresponding mathematically to stochastic differential equations conditioned on occupation measures. As an illustration, we consider the Langevin equation conditioned on staying for a fraction of time in different intervals of the real line, including the positive half-line which leads to a generalization of the Brownian meander problem. Other applications related to quasi-stationary distributions, metastable states, noisy chemical reactions, queues, and random walks are discussed.

Source: Journal of Mathematical Physics

DOI: 10.1063/1.4941384

Authors: Florian Angeletti, Hugo Touchette

Institutions: Stellenbosch University, National Institute for Theoretical Physics

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Research Foundation

Awards: G3846448975, G6944045144