Related papers: First Passage of a Randomly Accelerated Particle
We consider the dynamical evolution of a Brownian particle undergoing stochastic resetting, meaning that after random periods of time it is forced to return to the starting position. The intervals after which the random motion is stopped…
In this thesis, we develop analytical methods to study out-of-equilibrium stochastic processes driven by colored noise, i.e., noise with temporal correlations. These non-Markovian processes pose significant analytical challenges compared to…
We investigate the first-passage properties of bursty random walks on a finite one-dimensional interval of length L, in which unit-length steps to the left occur with probability close to one, while steps of length b to the right --…
We consider the moving particle process in Rd which is defined in the following way. There are two independent sequences (Tk) and (dk) of random variables. The variables Tk are non negative and form an increasing sequence, while variables…
A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of $N$ such events to occur is called an extreme first passage time. The rare event times are singular and limit…
The average velocity of self-propelled particles in a two-dimensional potential with colored noise is investigated. The current reversal phenomenon appear with changing x direction colored noise intensity. There exist optimal values of the…
We discuss the statistics of first-passage times of a Brownian particle moving in a highly unstable nonlinear potential proportional to an odd power of position. We observe temperature-induced shortening of the mean first-passage time and…
Examination of the free-fall motion of particles of extremely high-speed in the Schwarzschild geometry reveals that the gravitational acceleration of such particles is reversed when measured in Schwarzschild coordinates. High-speed…
We address some inverse problems for the first-passage place and the first-passage time of a one-dimensional diffusion process $\mathcal X(t)$ with stochastic resetting, starting from an initial position $\mathcal X(0)= \eta ;$ this type of…
We explore the properties of run-and-tumble particles moving in a piecewise-linear "ratchet" potential by deriving analytic results for the system's steady-state probability density, current, entropy production rate, extractable power, and…
We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…
We solve the problem of first-passage time for run-and-tumble particles in one dimension. Exact expression is derived for the mean first-passage time in the general case, considering external force-fields and chemotactic-fields, giving rise…
Given a Gaussian random walk (or a Wiener process), possibly with drift, observed through noise, we consider the problem of estimating its first-passage time $\tau_\ell$ of a given level $\ell$ with a stopping time $\eta$ defined over the…
Motivated by the dynamics of resonant neurons we consider a differentiable, non-Markovian random process $x(t)$ and particularly the time after which it will reach a certain level $x_b$. The probability density of this first passage time is…
A stochastic process with movement, return, and rest phases is considered in this paper. For the movement phase, the particles move following the dynamics of Gaussian process or ballistic type of L\'evy walk, and the time of each movement…
We formulate the first order Fermi acceleration in parallel shock waves in terms of the random walk theory. The formulation is applicable to any value of the shock speed and the particle speed, in particular to the acceleration in…
We consider the mean first passage time (MFPT) for a diffusive particle in a potential landscape with the extra condition that the particle is reset to its original position with some rate r. We study non-smooth and non-convex potentials…
We study the dynamics of a one-dimensional run and tumble particle subjected to confining potentials of the type $V(x) = \alpha \, |x|^p$, with $p>0$. The noise that drives the particle dynamics is telegraphic and alternates between $\pm 1$…
A common scenario in a variety of biological systems is that multiple particles are searching in parallel for an immobile target located in a bounded domain, and the fastest among them that arrives to the target first triggers a given…
Stochastic restart may drastically reduce the expected run time of a computer algorithm, expedite the completion of a complex search process, or increase the turnover rate of an enzymatic reaction. These diverse first-passage-time (FPT)…