Related papers: Formalization of Brownian motion in Lean
Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of…
A geometric p-rough path can be seen to be a genuine path of finite p-variation with values in a Lie group equipped with a natural distance. The group and its distance lift (R^{d},+,0) and its Euclidean distance. This approach allows us to…
We present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. Our result can be viewed as a new improvement to the LIL.
The balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences…
The first part of this paper is devoted to the Brown measure of the product of the free unitary Brownian motion by an arbitrary free non negative operator. Our approach follows the one recently initiated by Driver-Hall-Kemp though there are…
The invariance properties of Brownian motion are investigated and revisited within a recent Lie symmetry approach to stochastic differential equations. Some notable properties of the process can be recovered by a related integration by…
In this article, we study the extremal processes of branching Brownian motions conditioned on having an unusually large maximum. The limiting point measures form a one-parameter family and are the decoration point measures in the extremal…
The phenomenon of Brownian motion and Einstein's contribution to its understanding are introduced in a simple language.
We give a proof of a result on the growth of the number of particles along chosen paths in a branching Brownian motion. The work follows the approach of classical large deviations results, in which paths in $C[0,1]$ are rescaled onto…
We study a model for the entanglement of a two-dimensional reflecting Brownian motion in a bounded region divided into two halves by a wall with three or more small windows. We map the Brownian motion into a Markov Chain on the fundamental…
We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics. For this model, the total occupation measure is known to…
We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional L\'{e}vy's modulus of continuity and many other results are its particular cases.…
We construct a family of processes, from a single Poisson process, that converges in law to a complex Brownian motion. Moreover, we find realizations of these processes that converge almost surely to the complex Brownian motion, uniformly…
We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between dynamics of the particle and dynamic structure factor of the medium.
In this note, we combine the two approaches of Billingsley (1998) and Cs\H{o}rg\H{o} and R\'ev\'esz (1980), to provide a detailed sequential and descriptive for creating s standard Brownian motion, from a Brownian motion whose time space is…
In this paper we give some basic and important properties of several typical Banach spaces of functions of $G$-Brownian motion pathes induced by a sublinear expectation--G-expectation. Many results can be also applied to more general…
We briefly review the problem of Brownian motion and describe some intriguing facets. The problem is first treated in its original form as enunciated by Einstein, Langevin, and others. Then, utilizing the problem of Brownian motion as a…
Brownian motion whose infinitesimal variance changes according to a three-state continuous time Markov Chain is studied. This Markov Chain can be viewed as a telegraph process with one on state and two off states. We first derive the…
We give a complete characterisation of the domain of attraction of fixed points of branching Brownian motion (BBM) with critical drift. Prior to this classification, we introduce a suitable metric space of locally finite point measures on…
It has long been recognized that the dynamics of linear quantum systems is classical in the Wigner representation. Yet many conceptually important linear problems are typically analyzed using such generally applicable techniques as…