Related papers: The on/off Brownian snake
We study the problem of estimating a compact set $S\subset \mathbb{R}^d$ from a trajectory of a reflected Brownian motion in $S$ with reflections on the boundary of $S$. We establish consistency and rates of convergence for various…
The value of a continuous character evolving on a phylogenetic tree is commonly modelled as the location of a particle moving under one-dimensional Brownian motion with constant rate. The Brownian motion model is best suited to characters…
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.…
The first half of this chapter describes the development in mathematical models of Brownian motion after Einstein's seminal papers and current applications to optical tweezers. This instrument of choice among single-molecule biophysicists…
In this paper we introduce and study Brownian motion on state spaces with varying dimension. Starting with a concrete case of such state spaces that models a big square with a flag pole, we construct a Brownian motion on it and study how…
We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t)…
Soft robotic snakes made of compliant materials can continuously deform their bodies and, therefore, mimic the biological snakes' flexible and agile locomotion gaits better than their rigid-bodied counterparts. Without wheel support, to…
This note concerns distributions of Skew Brownian motion with dry friction and its occupation time. These distributions were obtained in [2] by using the Laplace transform and joint characteristic functions. We provide an alternative…
The problem of conditioning on the occupation field was investigated for the Brownian motion in 1998 independently by Aldous [4] and Warren and Yor [34] and recently for the loop soup at intensity $1/2$ by Werner [35], Sabot and Tarr\`es…
This article is a mathematical analysis of the Open Quantum Brownian Motion. This object was introduced by Bernard, Bauer, Benoist and Tilloy as the limit of a family of Open Quantum Random Walks on the discrete line. We prove the…
The primary purpose of this article is to prove a tightness of skew random walks. The tightness result implies, in particular, that the skew Brownian motion can be constructed as the scaling limit of such random walks. Our proof of…
We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By…
We investigate the large scale structure of certain sojourn sets of one dimensional Brownian motion within two-sided moving boundaries. The macroscopic Hausdorff dimension, upper mass dimension and logarithmic density of these sets are…
We study a modification of the fractional analogue of the Brownian meander, which is Brownian motion conditioned to be positive on the time interval ${[0,1]}$. More precisely, we determine the weak limit of a fractional Brownian motion…
This article contains both a point process and a sequential description of the greatest convex minorant of Brownian motion on a finite interval. We use these descriptions to provide new analysis of various features of the convex minorant…
The question how the extremal values of a stochastic process achieved on different time intervals are correlated to each other has been discussed within the last few years on examples of the running maximum of a Brownian motion, of a…
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This representation leads naturally to: - An efficient algorithm to…
A stochastic sewing lemma which is applicable for processes taking values in Banach spaces is introduced. Applications to additive functionals of fractional Brownian motion of distributional type are discussed.
A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian…
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.