Related papers: First Passage Time Densities in Resonate-and-Fire …
We provide exact results for the mean and variance of first-passage times (FPTs) of making a directed revolution in the presence of a bias in heterogeneous quenched environments where the disorder is expressed by random traps on a ring with…
A one-dimensional run-and-tumble particle (RTP) switches randomly between a left and right moving state of constant speed $v$. This type of motion arises in a wide range of applications in cell biology, including the unbiased growth and…
Making use of a Rice-like series expansion, for a class of stationary Gaussian processes the asymptotic behavior of the first passage time probability density function through certain time-varying boundaries, including periodic boundaries,…
We propose an analytical approach to study non-Markov random walks by employing an exact enumeration method. Using the method, we derive an exact expansion for the first-passage time (FPT) distribution for any continuous, differentiable…
We study the similarities and differences between different models concerning subdiffusion. More particularly, we calculate first passage time (FPT) distributions for subdiffusion, derived from Greens' functions of nonlinear equations…
Fractional Brownian motion is a generalised Gaussian diffusive process that is found to describe numerous stochastic phenomena in physics and biology. Here we introduce a multi-dimensional fractional Brownian motion (FBM) defined as a…
The study of first passage percolation (FPP) for the random interlacements model has been initiated in arXiv:2112.12096, where it is shown that on $\mathbb{Z}^d$, $d\geq 3$, the FPP distance is comparable to the graph distance with high…
Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first…
We consider a run-and-tumble particle (RTP) in one dimension, subjected to a telegraphic noise with a constant rate $\gamma$, and in the presence of an external confining potential $V(x) = \alpha |x|^p$ with $p \geq 1$. We compute the mean…
Renewal theory is finding increasing applications in non-equilibrium statistical physics. One example relates the probability density and survival probability of a Brownian particle or an active run-and-tumble particle with stochastic…
This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal firing probability density and an algorithm for the generation of sample-paths in order to construct…
The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by…
Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases.…
We prove that the first passage time density $\rho(t)$ for an Ornstein-Uhlenbeck process $X(t)$ obeying $dX=-\beta X dt + \sigma dW$ to reach a fixed threshold $\theta$ from a suprathreshold initial condition $x_0>\theta>0$ has a lower…
We study the statistical properties of first-passage Brownian functionals (FPBFs) of an Ornstein-Uhlenbeck (OU) process in the presence of stochastic resetting. We consider a one dimensional set-up where the diffusing particle sets off from…
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we…
We investigate the large deviation probabilities of first passage times (FPT) of discrete-time supercritical non-lattice branching random walks (BRWs) in $\mathbb{R}^d$ where $d\geq 1$. The FPT refers to the first time the BRW enters a ball…
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…
We investigate the statistics of the first-passage time (FPT) to a fractal self-similar boundary of the Koch snowflake. When the starting position is fixed near the absorbing boundary, the FPT distribution exhibits an apparent power-law…
Filtered shot noise processes have proven to be very effective in modelling the evolution of systems exposed to stochastic shot noise sources, and have been applied to a wide variety of fields ranging from electronics through biology. In…