Diffusions conditioned on occupation measures
Date
2016-02
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
AIP
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.
Description
CITATION: Angeletti, F. & Touchette, H. 2016. Diffusions conditioned on occupation measures. Journal of Mathematical Physics, 57, 023303, doi:10.1063/1.4941384.
The original publication is available at http://aip.scitation.org/journal/jmp
The original publication is available at http://aip.scitation.org/journal/jmp
Keywords
Markov, Markov processes, Diffusion -- Mathematical models
Citation
Angeletti, F. & Touchette, H. 2016. Diffusions conditioned on occupation measures. Journal of Mathematical Physics, 57, 023303, doi:10.1063/1.4941384.