Let D be the Wiener sausage of width " around two-sided Brownian motion. The components of 2-dimensional reeected Brownian motion in D converge to 1-dimensional Brownian motion and iterated Brownian motion, resp., as " goes to 0.

The viability of the time quantified Metropolis Monte Carlo technique to describe the dynamics of magnetic systems is discussed. Similar to standard Brownian motion, the method is introduced basing on the comparison between the Monte Carlo trial step and the mean squared deviation of the direction of the magnetic moment. The Brownian dynamics approach to the time evolution of a magnetic moment ...

This paper seeks to study standard Brownian motion and some of its properties. We construct this stochastic process and demonstrate a few properties including continuity and non-differentiability.

We solve the problem of formulating Brownian motion in a relativistically covariant framework in 1 + 1 and 3 + 1 dimensions. We obtain covariant Fokker-Planck equations with (for the isotropic case) a differential operator of invariant d'Alembert form. Treating the spacelike and timelike fluctuations separately, we show that it is essential to take into account the analytic continuation of " un...

This paper provides a an introduction to some basic properties of Brownian motion. In particular, it shows that Brownian motion exists, that Brownian motion is nowhere differentiability, and that Brownian motion has finite quadratic variation.

(To Appear) Stochastic Calculus for Brownian Motion on a Brownian Fracture By Davar Khoshnevisan* & Thomas M. Lewis University of Utah & Furman University Abstract. The impetus behind this work is a pathwise development of stochastic integrals with respect to iterated Brownian motion. We also provide a detailed analysis of the variations of iterated Brownian motion. These variations are linked ...