Related papers: Diffusion local time storage

In this article we study a homogeneous transient diffusion process $X$. We combine the theories of differential equations and of stochastic processes to obtain new results for homogeneous diffusion processes, generalizing the results of…

For a diffusion process $X(t)$ of drift $\mu(x)$ and of diffusion coefficient $D=1/2$, we study the joint distribution of the two local times $A(t)= \int_{0}^{t} d\tau \delta(X(\tau)) $ and $B(t)= \int_{0}^{t} d\tau \delta(X(\tau)-L) $ at…

In this paper, we analyze a discrete-time queue that is motivated from studying hospital inpatient flow management, where the customer count process captures the midnight inpatient census. The stationary distribution of the customer count…

In this paper we analyze the relaxation to steady-state of intracellular diffusion in a pair of cells with gap-junction coupling. Gap junctions are prevalent in most animal organs and tissues, providing a direct diffusion pathway for both…

We study a sequence of single server queues with customer abandonment (GI/GI/1+GI) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known ([20, 18]) that the…

Diffusion with stochastic resetting has recently emerged as a powerful modeling tool with a myriad of potential applications. Here, we study local time in this model, covering situations of free and biased diffusion with, and without, the…

We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of…

We study a class of Markov processes with finite state space and continuous time that have product form stationary distributions. We obtain a number of examples that can generate conjectures for diffusions with inert drift.

Diffusion with stochastic resetting, instantaneous returns of a diffusing particle to a reference point, creates a stationary probability distribution. The paradigm is extended here to a doubly stochastic protocol in which the resetting…

Consider a reflecting diffusion in a domain in $R^d$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the…

This note details the development of a discrete-time diffusion process to approximate the midnight customer count process in a $M_\textrm{per}/\textrm{Geo}_\textrm{2timeScale}/N$ system. We prove a limit theorem that supports this diffusion…

Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which…

A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…

A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…

Local time is the measure of how much time a random walk has visited a given position. In multiple scattering media, where waves are diffuse, local time measures the sensitivity of the waves to the local medium's properties. Local…

The entropy production rate is a central quantity in non-equilibrium statistical physics, scoring how far a stochastic process is from being time-reversible. In this paper, we compute the entropy production of diffusion processes at…

The effect of diffusional relaxation on the random sequential deposition process is studied in the limit of fast deposition. Expression for the coverage as a function of time are analytically derived for both the short-time and long-time…

A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…

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 consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…