Related papers: Inverse first-passage problems of a diffusion with…
In recent years, it has been well-established that adding a restart mechanism can alter the firstpassage statistics of a stochastic processes in useful and interesting ways. Though different mecha-nisms have been investigated, we derive a…
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…
Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an…
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 look into the problem of stochastic resetting with refractory periods. The model dynamics comprises diffusive and motionless phases. The diffusive phase ends at random time instants, at which the system is reset to a given position --…
We consider a random two-phase process which we call a reset-return one. The particle starts its motion at the origin. The first, displacement, phase corresponds to a stochastic motion of a particle and is finished at a resetting event. The…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
We consider a stochastic process undergoing resetting after which a random refractory period is imposed. In this period the process is quiescent and remains at the resetting position. Using a first-renewal approach, we compute exactly the…
Stochastic resetting can be naturally understood as a renewal process governing the evolution of an underlying stochastic process. In this work, we formally derive well-known results of diffusion with resets from a renewal theory…
This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…
In this paper we consider diffusion in a domain $\Omega$ containing a partially absorbing target $\calM$ with position and occupation time resetting. The occupation time $A_t$ is a Brownian functional that determines the amount of time that…
This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…
We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient $D(t) \sim t^{\alpha -1}$ with $\alpha > 0$ (scaled Brownian motion) is stochastically reset to its initial position,…
For a given barrier $S$ and a one-dimensional jump-diffusion process $X(t),$ starting from $x<S,$ we study the probability distribution of the integral $A_S(x)= \int_0 ^ {\tau_S(x)}X(t) \ dt$ determined by $X(t)$ till its first-crossing…
We study returns in dynamical systems: when a set of points, initially populating a prescribed region, swarms around phase space according to a deterministic rule of motion, we say that the return of the set occurs at the earliest moment…
Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately…
The initial inverse problem of finding solutions and their initial values ($t = 0$) appearing in a general class of fractional reaction-diffusion equations from the knowledge of solutions at the final time ($t = T$). Our work focuses on the…
We study experimentally, numerically and theoretically the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within a tolerance radius $R_{\text tol}$, a target at a distance $L$…
The inverse first-passage problem for a Wiener process $(W_t)_{t\ge0}$ seeks to determine a function $b{}:{}\mathbb{R}_+\to\mathbb{R}$ such that \[\tau=\inf\{t>0| W_t\ge b(t)\}\] has a given law. In this paper two methods for approximating…
We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this process is non-stationary and its probability…