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Monotonic continuous-time random walks with drift and stochastic reset events
Miquel Montero1, Javier Villarroel
1Departament de Física Fonamental, Universitat de Barcelona (UB), Martí i Franquès 1, E-08028 Barcelona, Spain. miquel.montero@ub.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 16, 2013
Summary
This study introduces a stochastic process with random resets, revealing unique statistical properties like power-law behavior and stable probability distributions. Monte Carlo simulations confirm these analytical findings for random walks with drift.
Area of Science:
- Statistical Physics
- Stochastic Processes
- Probability Theory
Background:
- Stochastic processes are fundamental in modeling complex systems.
- Understanding systems with reset events is crucial for various scientific domains.
- Monotonic random walks with drift exhibit unique statistical behaviors.
Purpose of the Study:
- To analyze statistical magnitudes of stochastic processes with random reset events.
- To investigate monotonic continuous-time random walks featuring constant drift.
- To derive general formulas for survival probability and mean exit time.
Main Methods:
- Analytical derivation of statistical properties for a stochastic process with resets.
- Focus on monotonic continuous-time random walks with constant drift.
- Validation using Monte Carlo simulations for numerical estimations.
Main Results:
- Emergence of a stationary transition probability density function for any drift strength.
- Demonstration of the model's capability to reproduce power-law-like behavior.
- Derivation of general formulas for survival probability and mean exit time.
Conclusions:
- The stochastic process with random resets exhibits novel statistical properties.
- Analytical predictions are robustly supported by independent Monte Carlo simulations.
- The model provides a framework for understanding systems with intermittent resets and drift.
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