相关论文: Large time probability of failure in diffusive sea…
We study the kinetics for the search of an immobile target by randomly moving searchers that detect it only upon encounter. The searchers perform intermittent random walks on a one-dimensional lattice. Each searcher can step on a nearest…
In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian--Caputo fractional…
In this paper, we investigate a Brownian motion (BM) with purely time dependent drift and difusion by suggesting and examining several Brownian functionals which characterize the lifetime and reactivity of such stochastic processes. We…
We consider a multidimensional search problem that is motivated by questions in contextual decision-making, such as dynamic pricing and personalized medicine. Nature selects a state from a $d$-dimensional unit ball and then generates a…
We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic…
We investigate the statistics of the local time $\mathcal{T} = \int_0^T \delta(x(t)) dt$ that a run and tumble particle (RTP) $x(t)$ in one dimension spends at the origin, with or without an external drift. By relating the local time to the…
We consider the paradigm of an overdamped Brownian particle in a potential well, which is modulated through an external protocol, in the presence of stochastic resetting. Thus, in addition to the short range diffusive motion, the particle…
Efficient spatial exploration is a key aspect of search and rescue. In this paper, we present a search algorithm that generates efficient trajectories that optimize the rate at which probability mass is covered by a searcher. This should…
The effects of a stochastic reset, to its initial configuration, is studied in the exactly solvable one-dimensional coagulation-diffusion process. A finite resetting rate leads to a modified non-equilibrium stationary state. If in addition…
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant…
We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that MSD relaxes to a constant only when the distribution of reset times possess finite mean and variance. In this case, the leading…
We solve a model of sluggish stochastic motion in which a Brownian particle diffuses with a diffusion coefficient that decays algebraically with the distance to the origin, as $|x|^{-\alpha}$. Additionally, the particle resets with a…
Let g : $\Omega$ = [0, 1] d $\rightarrow$ R denote a Lipschitz function that can be evaluated at each point, but at the price of a heavy computational time. Let X stand for a random variable with values in $\Omega$ such that one is able to…
In the past few years, stochastic resetting has become a subject of immense interest. Most of the theoretical studies so far focused on instantaneous resetting which is, however, a major impediment to practical realization or experimental…
We consider an anisotropic needle-like Brownian particle with nematic symmetry confined in a $2D$ domain. For this system, the coupling of translational and rotational diffusion makes the process ${\bf x} (t)$ of the positions of the…
Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time decoupled from the spatial position at the…
The canonical Evans--Majumdar model for diffusion with stochastic resetting to the origin assumes that resetting takes zero time: upon resetting the diffusing particle is teleported back to the origin to start its motion anew. However, in…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
We study a stochastic process where an active particle, modeled by a one-dimensional run-and-tumble particle, searches for a target with a finite absorption strength in thermal environments. Solving the Fokker-Planck equation for a uniform…
This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows that if the objective function exhibit multiscale…