First-passage properties of the jump process with a drift. The general case
arXiv:2510.17988 · doi:10.1088/1751-8121/ae485b
Abstract
We study the first-passage properties of a jump process with constant drift where jump amplitudes and inter-arrival times follow arbitrary light-tailed distributions with smooth densities. Using a mapping to an effective discrete-time random walk, we identify three regimes determined by the drift strength: survival (weak drift), absorption (strong drift), and critical. We derive explicit expressions for exponential decay rates in the survival and absorption regimes, and characterize algebraic decay at the critical point. We also obtain asymptotic behavior of the mean first-passage time, number of jumps, and their variances for processes starting either close to the origin or far from it.
65 pages, 17 figures, accepted version
References in corpus (34)
- Scaling description of the yielding transition in soft amorphous solids at zero temperature
- Wiener-Hopf factorization and distribution of extrema for a family of Lévy processes
- Monotonous continuous-time random walks with drift and stochastic reset events
- Universal survival probability for a -dimensional run-and-tumble particle
- Record statistics and persistence for a random walk with a drift
- From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of random walkers
- Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap
- Stochastic resetting by a random amplitude
- Universal Extremal Statistics in a Freely Expanding Jepsen Gas
- Survival probability of a run-and-tumble particle in the presence of a drift
- On the Gap and Time Interval between the First Two Maxima of Long Random Walks
- Role of initial conditions in diffusive systems: compressibility, hyperuniformity and long-term memory
- General flux to a trap in one and three dimensions
- Thermodynamic work of partial resetting
- Current fluctuations in stochastically resetting particle systems
- Effusion of stochastic processes on a line
- Random walks with stochastic resetting in complex networks: a discrete time approach
- Generalized disorder averages and current fluctuations in run and tumble particles
- First Passage Time for Many Particle Diffusion in Space-Time Random Environments
- Statistical properties of avalanches via the c-record process
- Local time of a system of Brownian particles on the line with steplike initial condition
- Resetting by rescaling: exact results for a diffusing particle in one-dimension
- Occupation time of a system of Brownian particles on the line with steplike initial condition
- Protocol dependence for avalanches under constant stress in elastoplastic models
- Macroscopic fluctuation theory of local time in lattice gases
- Large deviations in statistics of the local time and occupation time for a run and tumble particle
- Fastest first-passage time statistics for time-dependent particle injection
- Partial versus total resetting for Lévy flights in d dimensions: similarities and discrepancies
- Exact calculation of the mean first-passage time of continuous-time random walks by nonhomogeneous Wiener-Hopf integral equations
- The cost of resetting discrete-time random walks
- First-passage properties of the jump process with a drift. Two exactly solvable cases
- Uphill drift in the absence of current in single-file diffusion
- Effect of initial conditions on current fluctuations in non-interacting active particles
- A generating function approach to Markov chains undergoing binomial catastrophes