Microcanonical conditioning of Markov processes on time-additive observables

@article{Monthus2022MicrocanonicalCO,
  title={Microcanonical conditioning of Markov processes on time-additive observables},
  author={C. Monthus},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2022},
  volume={2022}
}
  • C. Monthus
  • Published 10 November 2021
  • Mathematics
  • Journal of Statistical Mechanics: Theory and Experiment
The recent study by De Bruyne et al (2021 J. Stat. Mech. 123204), concerning the conditioning of the Brownian motion and of random walks on global dynamical constraints over a finite time-window T, is reformulated as a general framework for the ‘microcanonical conditioning’ of Markov processes on time-additive observables. This formalism is applied to various types of Markov processes, namely discrete-time Markov chains, continuous-time Markov jump processes and diffusion processes in arbitrary… 
1 Citations
Optimal Resetting Brownian Bridges via Enhanced Fluctuations
We introduce a resetting Brownian bridge as a simple model to study search processes where the total search time t_{f} is finite and the searcher returns to its starting point at t_{f}. This is

References

SHOWING 1-10 OF 148 REFERENCES
Nonequilibrium Markov Processes Conditioned on Large Deviations
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
Large deviations for dynamical fluctuations of open Markov processes, with application to random cascades on trees
  • C. Monthus
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2018
The large deviations at 'Level 2.5 in time' for time-dependent ensemble-empirical-observables, introduced by C. Maes, K. Netocny and B. Wynants [Markov Proc. Rel. Fields. 14, 445 (2008)] for the case
Diffusions conditioned on occupation measures
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
Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
The Ruelle thermodynamic formalism for dynamical trajectories over the large time T corresponds to the large deviation theory for the information per unit time of the trajectories probabilities. The
Large deviations for Markov processes with stochastic resetting: analysis via the empirical density and flows or via excursions between resets
Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at
Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment
  • C. Monthus
  • Mathematics
    Journal of Statistical Mechanics: Theory and Experiment
  • 2022
The large deviations at level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their
Strongly constrained stochastic processes: the multi-ends Brownian bridge
In a recent article, Krapivsky and Redner (J. Stat. Mech. 093208 (2018)) established that the distribution of the first hitting times for a diffusing particle subject to hitting an absorber is
Large deviations conditioned on large deviations I: Markov chain and Langevin equation
We present a systematic analysis of stochastic processes conditioned on an empirical observable $$Q_T$$QT defined in a time interval [0, T], for large T. We build our analysis starting with a
Variational and optimal control representations of conditioned and driven processes
TLDR
These interpretations of the driven process generalize and unify many previous results on maximum entropy approaches to nonequilibrium systems, spectral characterizations of positive operators, and control approaches to large deviation theory and lead to new methods for analytically or numerically approximating large deviation functions.
...
...