Related papers: Brownian Motion - Past and Present
Active Brownian motion is the complex motion of active Brownian particles. They are active in the sense that they can transform their internal energy into energy of motion and thus create complex motion patterns. Theories of active Brownian…
An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The…
The Klein-Kramers equation, governing the Brownian motion of a classical particle in quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large…
Starting with a Brownian motion, we define and study a novel diffusion process by combining stickiness and oscillation properties. The associated stochastic differential equation, resolvent and semigroup are provided. Also the trivariate…
The first comprehensive overview of the final version of the general theory of relativity was published by Einstein in 1916 after several expositions of preliminary versions and latest revisions of the theory in November 1915. A historical…
We characterize the asymptotic behaviour of the weighted power variation processes associated with iterated Brownian motion. We prove weak convergence results in the sense of finite dimensional distributions, and show that the laws of the…
We construct a theory for the 1+1-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity, and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the…
We attempt to see how closely we can formally obtain the planetary and light path equations of General Relativity by employing certain operations on the familiar Newtonian equation. This article is intended neither as an alternative to nor…
Let B_1,B_2, ... be independent one-dimensional Brownian motions defined over the whole real line such that B_i(0)=0. We consider the nth iterated Brownian motion W_n(t)= B_n(B_{n-1}(...(B_2(B_1(t)))...)). Although the sequences of…
A fully quantum treatment of Einstein's Brownian motion is given, showing in particular the role played by the two original requirements of translational invariance and connection between dynamics of the Brownian particle and atomic nature…
This is a brief presentation of historical introduction to the theoretical concept of neutrino oscillation during the early stage up to 60's. (Openig address at the Europhysics NEUTRINO OSCILLATION WORKSHOP (NOW' 98), 7-9 Sept. 1998,…
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 situation with respect to the experiments is presented of a recently proposed model that gives an explanation of the Pioneer anomalous acceleration $a_{\rm P}$. The model is based on an idea already discovered by Einstein in 1907: the…
Einstein, in his "Zur Elektrodynamik bewegter Korper", gave a physical (operational) meaning to "time" of a remote event in describing "motion" by introducing the concept of "synchronous stationary clocks located at different places". But…
Brownian motion provides a bedrock for the understanding of soft condensed matter and, therefore, of the physical description of the microscopic biological world. Inspired by this domain, and combining softness with hydrodynamic energy…
This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated…
The Liouville Brownian motion was introduced in \cite{GRV} as a time changed process $B_{A_t^{-1}}$ of a planar Brownian motion $(B_t)_{t \ge 0}$, where $(A_t)_{t \ge 0}$ is the positive continuous additive functional of $(B_t)_{t \ge 0}$…
The integrated Brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first…
This review describes the discovery of gravitational waves. We recount the journey of predicting and finding those waves, since its beginning in the early twentieth century, their prediction by Einstein in 1916, theoretical and experimental…
Let $B=(B_t)_{t\geq 0}$ be a standard Brownian motion. The main objective is to find a uniform (in time) control of the modulus of continuity of $B$ in the spirit of what appears in (Kurtz, 1978). More precisely, it involves the control of…