Monotonous continuous-time random walks with drift and stochastic reset events

Abstract

In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous continuous-time random walks with a constant drift: the process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence|for any drift strength|of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

15 pages, 4 figures, revtex4-1; considerable revision, 4 appendices added

References in corpus (14)

• Diffusion with Stochastic Resetting
• Diffusion with Optimal Resetting
• Diffusion of Earthquake Aftershock Epicenters, Omori's Law and Generalized Continuous-Time Random Walk Models
• Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation
• Multiplicative processes and power laws
• A continuous time random walk model for financial distributions
• Power-Law Time Distribution of Large Earthquakes
• Stochastic multiplicative processes with reset events
• The continuous time random walk formalism in financial markets
• Long-Tailed Trapping Times and Levy Flights in a Self-Organized Critical Granular System
• Scaling and data collapse for the mean exit time of asset prices
• Extreme times in financial markets
• On the effect of random inhomogeneities in Kerr-media modelled by non-linear Schrodinger equation
• Exit times in non-Markovian drifting continuous-time random walk processes

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• Comparison of two models of tethered motion
• Diffusion processes with Gamma-distributed resetting and non-instantaneous returns
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• Informational and Causal Architecture of Discrete-Time Renewal Processes
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Non-equilibrium thermodynamics of diffusion in fluctuating potentials
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• Statistical Signatures of Structural Organization: The case of long memory in renewal processes
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• Striking universalities in stochastic resetting processes
• Non-linear diffusion with stochastic resetting
• Mean-performance of Sharp Restart II: Inequality Roadmap
• Fat Tails and Black Swans: Exact Results for Multiplicative Processes with Resets
• Discrete-time random walks and Lévy flights on arbitrary networks: when resetting becomes advantageous?
• Tail-behavior roadmap for sharp restart
• Optimal potentials for diffusive search strategies
• A computational framework for two-dimensional random walks with restarts
• Measurement-induced resetting in open quantum systems
• Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity
• First-passage properties of the jump process with a drift. Two exactly solvable cases
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