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Article Dans Une Revue Journal of Statistical Physics Année : 2019

Large deviations conditioned on large deviations I: Markov chain and Langevin equation

Résumé

We present a systematic analysis of stochastic processes conditioned on an empirical observable QT defined in a time interval [0, T], for large T. We build our analysis starting with a discrete time Markov chain. Results for a continuous time Markov process and Langevin dynamics are derived as limiting cases. In the large T limit, we show how conditioning on a value of QT modifies the dynamics. For a Langevin dynamics with weak noise and conditioned on QT, we introduce large deviation functions and calculate them using either a WKB method or a variational formulation. This allows us, in particular, to calculate the typical trajectory and the fluctuations around this trajectory when conditioned on a certain value of QT, for large T.

Dates et versions

hal-02367892 , version 1 (18-11-2019)

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Bernard Derrida, Tridib Sadhu. Large deviations conditioned on large deviations I: Markov chain and Langevin equation. Journal of Statistical Physics, 2019, 176 (4), pp.773-805. ⟨10.1007/s10955-019-02321-4⟩. ⟨hal-02367892⟩
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