Introduction. Let (Ω,F ,P) be a probability space, B = (Bt)t≥0 a Brownian motion defined on this space, with values in Rd. (Ft)t≥0 is the standard filtration of the Brownian motion. Also given are τ a {Ft}-stopping time, ξ a real, Fτ -measurable random variable, called the final condition, and f :Ω× R+ × R×Rd → R the generator. We wish to find a progressively measurable solution (Y,Z), with val...

Local Times of Brownian Motion were introduced in 1948 by French mathematician Paul Lévy in his fundamental book Processus Stochastiques et Mouvement Brownien. Naturally arising in many problems (such as, for instance, an extension of Itô’s formula to convex functions, or finding the density of the occupation measure of BM with respect to the Lebesgue measure), they also roughly describe the am...

In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area) A(T ), covered by the process in the time interval [0, T ]. The Laplace transform of A(T ) follows as a consequence. The main proof involves a double Laplace transform of A(T ) and is based on excursion theory and local time for Browni...

Abstract We prove that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean. We show that under suitable conditions, when T has heavy tails the scaling limit is the so-called fractional kinetics process, a random time-change of Brownian motion. The proof uses the standard tools of time-change and invarian...

in this paper the effect of using various models for conductivity and viscosity considering brownian motion of nanoparticles is investigated. this study is numerically conducted inside a cavity full of water-al2o3 nanofluid at the case of mixed convection heat transfer. the effect of some parameters such as the nanoparticle volume fraction, rayleigh, richardson and reynolds numbers has been exa...

This paper is concerned with the mathematical analysis of terminal value problems (TVP) for a stochastic nonclassical diffusion equation, where source assumed to be driven by classical and fractional Brownian motions (fBms). Our two are study in sense well-posedness ill-posedness meanings. Here, TVP problem determining statistical properties initial data from final time data. In case [Formula: ...

langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. the brownian motion generated from molecular bombardment was taken as a wiener stochastic process and approximated by a gaussian white noise. euler-maruyama method was used to solve the langevin equation numerically. the accuracy of brownian simulation was checked by performing a series of simulati...