Related papers: Brownian Motion for the School-Going Child
We provide a new and elementary proof of Levy's second arcsine law for Brownian motion. The only tools required are basic properties of Brownian motion and Poisson processes, and the ballot theorem. Our proof is readily extended to Brownian…
Wellness and mindfulness act as buzzwords these days, often seen as separate from physics. Yet we know they are important, and everything is related to physics! In this article, we will consider a few simple classroom activities that can…
We stress the relevance of the two features of translational invariance and atomic nature of the gas in the quantum description of the motion of a massive test particle in a gas, corresponding to the original picture of Einstein used in the…
In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was…
We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of the distribution, both for one-sided and two-sided Brownian…
A theoretical parallel between the classical Brownian motion and quantum mechanics is explored. It is shown that, in contrast to the classical Langevin force, quantum mechanics is driven by turbulent velocity fluctuations with diffusive…
The Einstein-First project approaches the teaching of Einsteinian physics through the use of physical models and analogies. This paper presents an approach to the teaching of quantum physics which begins by emphasising the particle-nature…
Brownian motion is a building block in modern probability theory. In this paper, we describe a formalization of Brownian motion using the Lean theorem prover. We build on the existing measure-theoretic foundations in Lean's mathematical…
We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…
This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numerical simulation motivates this survey. This article ends with…
The motion of a particle under the influence of a dynamical disorder is described by the DLD model. One motivation is to understand the motion of an electron inside a metal; Another is to understand quantal Brownian motion. The overview is…
We describe a simple numerical simulation, suitable for an undergraduate project (or graduate problem set), of the Brownian motion of a particle in a Hooke-law potential well. Understanding this physical situation is a practical necessity…
The evolution of prices on ideal market is given by geometrical Brownian motion, where Gaussian white noise describes fluctuations. We study the effect of correlations introduced by a color noise.
We define bi-monotone independence, prove a bi-monotone central limit theorem and use it to study the distribution of bi-monotone Brownian motion, which is defined as the two-dimensional operator process with monotone and antimonotone…
The indefinite integral of the homogenized Ornstein-Uhlenbeck process is a well-known model for physical Brownian motion, modelling the behaviour of an object subject to random impulses [L. S. Ornstein, G. E. Uhlenbeck: On the theory of…
We propose new equations of motion under the theory of the Brownian motion to connect the states of quantum, diffusion, soliton, and periodic localization. The new equations are nothing but the classical equations of motion with two…
Tracking a real trajectory of a quantum particle still has been treated as the interpretation problem. It shall be expressed by a Brownian (stochastic) motion suggested by E. Nelson, however, the well-defined mechanism of field generation…
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…
This paper studies Brownian motion subject to the occurrence of a minimal length excursion below a given excursion level. The law of this process is determined. The characterization is explicit and shows by a layer construction how the law…
We construct Brownian motion on a wide class of metric spaces similar to graphs, and show that its cover time admits an upper bound depending only on the length of the space.