相关论文: On Maximum Increase and Decrease of Brownian Motio…

We outline a reduction scheme for a class of Brownian dynamics which leads to meaningful corrections to the Smoluchowski equation in the overdamped regime. The mobility coefficient of the reduced dynamics is obtained by exploiting the…

This paper deals with the problems of consistence and strong consistence of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. A central limit theorem for…

Prompted by an example arising in critical percolation, we study some reflected Brownian motions in symmetric planar domains and show that they are intertwined with one-dimensional diffusions. In the case of a wedge, the reflected Brownian…

We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…

We study the motion of an elastic object driven in a disordered environment in presence of both dissipation and inertia. We consider random forces with the statistics of random walks and reduce the problem to a single degree of freedom. It…

We provide upper and lower bounds for the mean ${\mathscr M}(H)$ of $\sup_{t\geqslant 0} \{B_H(t) - t\}$, with $B_H(\cdot)$ a zero-mean, variance-normalized version of fractional Brownian motion with Hurst parameter $H\in(0,1)$. We find…

We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of…

The fractional Brownian motion of index $0 < H < 1$, H-FBM, with d-dimensional time is considered on an expanding set TG, where G is a bounded convex domain that contains 0 at its boundary. The main result: if 0 is a point of smoothness of…

We formulate and solve a variant of the quickest detection problem which features false negatives. A standard Brownian motion acquires a drift at an independent exponential random time which is not directly observable. Based on the…

The purpose of the paper is to find the joint distribution of the hitting time and place of two-dimensional Brownian motion hitting the negative horizontal axis. We provide various formulas for Green functions as well as for the conditional…

Basic properties of Brownian motion are used to derive two results concerning birth-death chains. First, the probability of extinction is calculated. Second, sufficient conditions on the transition probabilities of a birth-death chain are…

By using the Kirkwood formula, the friction coefficient of a solvated Brownian particle is determined from the integration on time of the autocorrelation function of the force that the solvent exerts on this particle. Extensive molecular…

In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…

Consider a generic triangle in the upper half of the complex plane with one side on the real line. This paper presents a tailored construction of a discrete random walk whose continuum limit is a Brownian motion in the triangle, reflected…

For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $\mu(x)$ and $\sigma^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip…

Consider a Brownian motion on the circumference of the unit circle, which jumps to the opposite point of the circumference at incident times of an independent Poisson process of rate $\lambda$. We examine the problem of coupling two copies…

We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that…

We consider n non-intersecting Brownian motion paths with p prescribed starting positions at time t=0 and q prescribed ending positions at time t=1. The positions of the paths at any intermediate time are a determinantal point process,…

We consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spendings/dividend payments,…

We consider certain noncolliding interacting particle systems driven by Brownian noise. A key example is drifted Brownian motions conditioned not to intersect and related models of eigenvalues of Hermitian random matrices. We establish…