Related papers: First-passage time statistics for non-linear diffu…
A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…
We consider a non-Gaussian stochastic process where a particle diffuses in the $y$-direction, $dy/dt=\eta(t)$, subject to a transverse shear flow in the $x$-direction, $dx/dt=f(y)$. Absorption with probability $p$ occurs at each crossing of…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
Consider a stable L\'evy process $X=(X_t,t\geq 0)$ and let $T_x$, for $x>0$, denote the first passage time of $X$ above the level $x$. In this work, we give an alternative proof of the absolute continuity of the law of $T_x$ and we obtain a…
Stochastic resetting has emerged as a useful strategy to reduce the completion time for a broad class of first passage processes. In the canonical setup, one intermittently resets a given system to its initial configuration only to start…
We derive the probability density of a diffusion process generated by nonergodic velocity fluctuations in presence of a weak potential, using the Liouville equation approach. The velocity of the diffusing particle undergoes dichotomic…
The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal…
Fluids confined to quasi-one-dimensional channels exhibit a dynamic crossover from single file diffusion to normal diffusion as the channel becomes wide enough for particles to hop past each other. In the crossover regime, where hopping…
We investigate the first-passage dynamics of symmetric and asymmetric L\'evy flights in a semi-infinite and bounded intervals. By solving the space-fractional diffusion equation, we analyse the fractional-order moments of the first-passage…
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter…
We investigate a class of diffusion-controlled reactions that are initiated at the time instance when a prescribed number $K$ among $N$ particles independently diffusing in a solvent are simultaneously bound to a target region. In the…
In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…
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 consider a Brownian particle diffusing in a one dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive…
Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution of first passage time, and in particular the mean first…
We study the statistics of last-passage time for linear diffusions. First we present an elementary derivation of the Laplace transform of the probability density of the last-passage time, thus recovering known results from the mathematical…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…