相关论文: First exit of Brownian motion from a one-sided mov…

Motivated by an approximation problem from mathematical finance, we analyse the stability of the boundary crossing probability for the multivariate Brownian motion process, with respect to small changes of the boundary. Under broad…

We study the norm of the two-dimensional Brownian motion conditioned to stay outside the unit disk at all times. By conditioning the process is changed from barely recurrent to slightly transient. We obtain sharp results on the rate of…

We consider the one-sided exit problem for fractional Brownian motion (FBM), which is equivalent to the question of the distribution of the lower tail of the maximum of FBM on the unit interval. We improve the bounds given by Molchan (1999)…

We consider a fractional Brownian motion with unknown linear drift such that the drift coefficient has a prior normal distribution and construct a sequential test for the hypothesis that the drift is positive versus the alternative that it…

A well-known result with respect to the one dimensional nearest-neighbor symmetric simple exclusion process is the convergence to fractional Brownian motion with Hurst parameter 1/4, in the sense of finite-dimensional distributions, of the…

Based on an optimal rate wavelet series representation, we derive a local modulus of continuity result with a refined almost sure upper bound for fractional Brownian motion. \sloppy The obtained upper bound of the small fractional Brownian…

We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically…

We consider various problems related to the persistence probability of fractional Brownian motion (FBM), which is the probability that the FBM $X$ stays below a certain level until time $T$. Recently, Oshanin et al. study a physical model…

We construct a Bayesian sequential test of two simple hypotheses about the value of the unobservable drift coefficient of a Brownian motion, with a possibility to change the initial decision at subsequent moments of time for some penalty.…

We study the asymptotic behaviour of the tail of the distribution of the first passage time of a L\'evy process over a one-sided moving boundary. Our main result states that if the boundary behaves as $t^{\gamma}$ for large $t$ for some…

Consider the first exit time of one-dimensional Brownian motion $\{B_s\}_{s\geq 0}$ from a random passageway. We discuss a Brownian motion with two time-dependent random boundaries in quenched sense. Let $\{W_s\}_{s\geq 0}$ be an other…

In [4], it is proved that we can have a continuous first-passage-time density function of one dimensional standard Brownian motion when the boundary is H\"older continuous with exponent greater than 1/2. For the purpose of extending [4]…

We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior…

The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the…

Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases.…

In this note we investigate the behaviour of Brownian motion conditioned on a growth constraint of its local time which has been previously investigated by Berestycki and Benjamini. For a class of non-decreasing positive functions $f(t);…

The narrow escape problem is a first-passage problem concerned with randomly moving particles in a physical domain, being trapped by absorbing surface traps (windows), such that the measure of traps is small compared to the domain size. The…

We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space. This process is a generalization of the set-indexed Brownian motion, when the condition of independance is…

We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate in Poissonian obstacles exits a large domain. Results are formulated in terms of the solution to a semilinear partial…

We study a space-time Brownian motion with drift B(t)=(t_0+t,y_0+W(t)+t) killed at the moving boundary of the cone {(t,x):0<x<t}. This article determines the parabolic Martin boundary and all harmonic functions associated with this process.…