Related papers: Mirror transitions in diffusion with stochastic re…
We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…
First passage phenomena arise across physics, biology, and finance when stochastic processes first reach a threshold, triggering downstream events. Examples include the irreversible exit from a domain, a biochemical reaction, a financial…
We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
We investigate restricted diffusion in a bounded domain towards a small partially reactive target in three- and higher-dimensional spaces. We propose a simple explicit approximation for the principal eigenvalue of the Laplace operator with…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of…
Classical first passage under resetting is a paradigm in the search process. Despite its multitude of applications across interdisciplinary sciences, experimental realizations of such resetting processes posit practical challenges in…
We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in…
Resetting a stochastic process is an important problem describing the evolution of physical, biological and other systems which are continually returned to their certain fixed point. We consider the motion of a subdiffusive particle with a…
A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…
We consider motion of an overdamped Brownian particle subject to stochastic resetting in one dimension. In contrast to the usual setting where the particle is instantaneously reset to a preferred location (say, the origin), here we consider…
We study the first hitting time statistics between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of the…
The transport of particles through channels holds immense significance in physics, chemistry, and biological sciences. For instance, the motion of solutes through biological channels is facilitated by specialized proteins that create…
We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…
We consider a run-and-tumble particle on a half-line with an absorbing target at the origin. The particle has an internal velocity state that switches between two opposite values at Poisson-distributed times. The position of the particle…
Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach…
The Ornstein-Uhlenbeck process of diffusion in the harmonic potential is re-examined in the context of the first-passage time problem. We investigate this problem to the extent that it has not yet been fully resolved and demonstrate exact…
The study of diffusion with preferential returns to places visited in the past has attracted an increased attention in recent years. In these highly non-Markov processes, a standard diffusive particle intermittently resets at a given rate…