Related papers: A density for the local time of the Brox diffusion
Statistical moments of the intensity distributions are used as molecular descriptors. They are used as a basis for defining similarity distances between two model spectra. Parameters which carry the information derived from the comparison…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
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…
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…
The fundamental solutions of diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences…
We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of the distribution, both for one-sided and two-sided Brownian…
We study the distribution of the time to explosion for one-dimensional diffusions. We relate this question to computing the expectations of suitable nonnegative local martingales, and to the distributions of related diffusions with unit…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
The definition of local spatial densities by using sharply localized one-particle states is applied to spin-3/2 systems. Matrix elements of the electromagnetic current and the energy-momentum tensor are considered and integral expressions…
Advection and dispersion in highly heterogeneous environments involving interfacial discontinuities in the corresponding drift and dispersion rates are described through disparate examples from the physical and biological sciences. A…
We assume that we observe $N$ independent copies of a diffusion process on a time-interval $[0,2T]$. For a given time $t$, we estimate the transition density $p_t(x,y)$, namely the conditional density of $X_{t + s}$ given $X_s = x$, under…
An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The…
We are concerned with the first hitting times of the Bessel processes. We give explicit expressions for the densities by means of the zeros of the Bessel functions and show their asymptotic behavior.
Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of…
In this paper we study a storage process or a liquid queue in which the input process is the local time of a positively recurrent stationary diffusion in stationary state and the potential output takes place with a constant deterministic…
We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we…
We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions and for the densities by means of the zeros of the Bessel functions. The results extend the classical ones and cover…
The purpose of this article is to give another proof on the existence of a diffusion on a junction, which has been already done by M.Freidlin and S-J.Sheu, in Diffusion processes on graphs, (2000). We generalize the result to time dependent…
We assume that a finite set of moments of a random vector is given. Its underlying density is unknown. An algorithm is proposed for efficiently calculating Dirac mixture densities maintaining these moments while providing a homogeneous…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…