Related papers: Some explicit formulas for the Brownian bridge, Br…
Brownian and fractional processes are useful computational tools for the modelling of physical phenomena. Here, modelling linear homopolymers in solution as Brownian or fractional processes, we develop a formalism to take into account both…
For a Brownian bridge from $0$ to $y$ we prove that the mean of the first exit time from interval $(-h,h), \,\, h>0,$ behaves as $O(h^2)$ when $h \downarrow 0.$ Similar behavior is seen to hold also for the 3-dimensional Bessel bridge. For…
Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…
In this paper, we study the asymptotic behavior of the number of crossings by a one-dimensional diffusion of a threshold where the process exhibits stickiness. We distinguish three types of crossings and show that to each type corresponds a…
This paper develops some general calculus for GGC and Dirichlet process means functionals. It then proceeds via an investigation of positive Linnik random variables, and more generally random variables derived from compositions of a stable…
We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The…
This survey is a collection of various results and formulas by different authors on the areas (integrals) of five related processes, viz.\spacefactor =1000 Brownian motion, bridge, excursion, meander and double meander; for the Brownian…
In this paper we study periodical stochastic processes, and we define the conditions that are needed by a model to be a good noise model on the circumference. The classes of processes that fit the required conditions are studied together…
We consider a one dimensional random-walk-like process, whose steps are centered Gaussians with variances which are determined according to the sequence of arrivals of a Poisson process on the line. This process is decorated by independent…
Sampling formulas describe probability laws of exchangeable combinatorial structures like partitions and compositions. We give a brief account of two known parametric families of sampling formulas and add a new family to the list.
A new formula for the probability that a standard Brownian motion stays between two linear boundaries is proved. A simple algorithm is deduced. Uniform precision estimates are computed. Different implementations have been made available…
A construction of $p$-parameter Brownian sheet on the hypercube $C=[0,1]^p$ as a sum of $2^p$ independent Gaussian processes is obtained. The terms are closely related to Brownian pillows, and the probability laws of their $L^2(C)$ squared…
We study sample path deviations of the Wiener process from three different representations of its bridge: anticipative version, integral representation and space-time transform. Although these representations of the Wiener bridge are equal…
A Monte Carlo method for simulating a multi-dimensional diffusion process conditioned on hitting a fixed point at a fixed future time is developed. Proposals for such diffusion bridges are obtained by superimposing an additional guiding…
In this paper we establish relationships between four important concepts: (a) hitting time problems of Brownian motion, (b) 3-dimensional Bessel bridges, (c) Schr\"odinger's equation with linear potential, and (d) heat equation problems…
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to…
We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on…
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class…
We provide a representation of the maximal difference between a standard Brownian bridge and its concave majorant on the unit interval, from which we deduce expressions for the distribution and density functions and moments of this…
Nonintersecting Brownian bridges on the unit circle form a determinantal stochastic process exhibiting random matrix statistics for large numbers of walkers. We investigate the effect of adding a drift term to walkers on the circle…