Related papers: Exact simulation of first exit times for one-dimen…
We study a generalized geometric Brownian motion framework that incorporates both entries of new units and exit mechanisms for the current population, extending earlier stochastic resetting models where these rates are treated as identical.…
We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem…
In this note, by an elementary use of Girsanov's transform we show that the exit time for either a biased random walk or a drifted Brownian motion on a symmetric interval is stochastically monotone with respect to the drift parameter. In…
This article presents a review of some old and new results on the long time behavior of reflected diffusions. First, we present a summary of prior results on construction, ergodicity and geometric ergodicity of reflected diffusions in the…
We study experimentally and theoretically the optimal mean time needed by a free diffusing Brownian particle to reach a target at a distance L from an initial position in the presence of resetting. Both the initial position and the…
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…
Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space,…
The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles…
We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be…
In this paper we introduce modified version of one-dimensional outflow dynamics (known as a Sznajd model) which simplifies the analytical treatment. We show that simulations results of the original and modified rules are exactly the same…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
By considering any one-dimensional time-homogeneous solvable diffusion process,this paper develops a complete analytical framework for computing the distribution of the last hitting time, to any level, and its joint distribution with the…
For $d\ge1$ and $r>0$, let $X^{(d;r)}(\cdot)$ be a $d$-dimensional Brownian motion with diffusion coefficient $D$, equipped with an exponential clock with rate $r$. When the clock rings, the process jumps to the origin and begins anew. For…
We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the $n$th-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM,…
The {\alpha}-stable L\'evy process, commonly used to describe L\'evy flight, is characterized by discontinuous jumps and is widely used to model anomalous transport phenomena. In this study, we investigate the associated exit problem and…
A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
In this paper we develop a probabilistic model of single-particle diffusion in 1D multi-layered media by constructing a multi-layered version of so-called snapping out Brownian motion (BM). The latter sews together successive rounds of…
We study the narrow escape problem in the disk, which consists in identifying the first exit time and first exit point distribution of a Brownian particle from the ball in dimension 2, with reflecting boundary conditions except on small…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…