Related papers: Approximate calculation of multidimensional first …
Recently a general growth curve including the well known growth equations, such as Malthus, logistic, Bertallanfy, Gompertz, has been studied. We now propose two stochastic formulations of this growth equation. They are obtained starting…
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from…
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…
The time-dependent barrier passage of an anomalous damping system is studied via the generalized Langevin equation (GLE) with non-Ohmic memory damping friction tensor and corresponding thermal colored noise tensor describing a particle…
We derive bridges from general multidimensional linear non time-homogeneous processes using only the transition densities of the original process giving their integral representations (in terms of a standard Wiener process) and so-called…
We propose a model for anomalous transport in inhomogeneous environments, such as fractured rocks, in which particles move only along pre-existing self-similar curves (cracks). The stochastic Loewner equation is used to efficiently generate…
Gated first-passage processes, where completion depends on both hitting a target and satisfying additional constraints, are prevalent across various fields. Despite their significance, analytical solutions to basic problems remain unknown,…
The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which is based on the starting value of the boundary to a smooth…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
This paper is concerned with the two--phase obstacle problem, a type of a variational free boundary problem. We recall the basic estimates of Repin and Valdman (2015) and verify them numerically on two examples in two space dimensions. A…
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…
We propose an approach for estimating the probability that a given small target, among many, will be the first to be reached in a molecular dynamics simulation. Reaching small targets out of a vast number of possible configurations…
We study the Darcy boundary value problem with log-normal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the…
We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of…
We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem…
We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…