Related papers: Brownian Motion for the School-Going Child
We establish diffusion and fractional Brownian motion approximations for motions in a Markovian Gaussian random field with a nonzero mean.
The $n$th order fractional Brownian motion was introduced by Perrin et al. It is the (upto a multiplicative constant) unique self-similar Gaussian process with Hurst index $H \in (n-1,n)$, having $n$th order stationary increments. We…
Tempered fractional Brownian motion is revisited from the viewpoint of reduced fractional Ornstein-Uhlenbeck process. Many of the basic properties of the tempered fractional Brownian motion can be shown to be direct consequences or…
A description of motion is proposed, adapted to the composite bundle interpretation of Poincar\'e Gauge Theory. Reference frames, relative positions and time evolution are characterized in gauge-theoretical terms. The approach is…
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…
Einstein's 1905 analysis of the Brownian Motion of a pollen grain in a water droplet as due to statistical variations in the collisions of water molecules with the grain, followed up by Perrin's experiments, provided one of the most…
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…
Consider the $\lambda$-Green function and the $\lambda$-Poisson kernel of a Lipschitz domain $U\subset \mathbb H^n=\left\{x\in\mathbb R^n:x_n>0\right\}$ for hyperbolic Brownian motion with drift. We provide several relationships that…
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…
We present a duality relation between two systems of coalescing random walks and an analogous duality relation between two systems of coalescing Brownian motions. Our results extends previous work in the literature and we apply it to the…
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.
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…
Modification of three ideas underlying Newton's original world view, with only minor changes in context, might offer two advantages to introductory physics students. First, the students will experience less cognitive dissonance when they…
In the air surrounding us, how does a particle diffuse? Thanks to Einstein and other pioneers,it has been well known that generally the particle will undergo the Brownian motion, and in the last century this insight has been corroborated by…
We study the fluctuations of the power variation of fractional Brownian motion in Brownian time
In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…
We review our investigations on Gibbs measures relative to Brownian motion, in particular the existence of such measures and their path properties, uniqueness, resp. non-uniqueness. For the case when the energy only depends on increments,…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
Brownian motions on a metric graph are defined, their Feller property is proved, and their generators are characterized. This yields a version of Feller's theorem for metric graphs.
We perform an analysis where Einstein's field equation is derived by means of very simple thermodynamical arguments. Our derivation is based on a consideration of the properties of a very small, spacelike two-plane in a uniformly…