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

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.

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.

Geometric object detection has many applications, such as in tracking. Particle tracking microrheology is a technique for studying mechanical properties by accurately tracking the motion of the immersed particles undergoing Brownian motion. Since particles are carried along by these random undulations of the medium, they can move in and out of the microscopeʹs...

(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 ...

The ruin probability of the reserve of an insurance company, in finite and infinite horizon, when there is the possibility to invest in a risky asset, has recently received a lot of attention. It is well known that for the classical Cramér-Lundberg process (where there is no investment and the claims have exponential moments), the ruin probability decreases exponentially with respect to the ini...

The price on the electricity market is constantly changing. Owing to characteristics of future movement relatively hard predict. For this reason following three processes are applied: process according geometric Brownian motion, mean reversion process, and spikes process. paper discusses all processes, including their definitions, formulas applications, as well upsides downsides.