Exact distribution of the Generalized Shiryaev–Roberts stopping time under the minimax Brownian motion setup

Existence Conditions of the Optimal Stopping Time: the Cases of Geometric Brownian Motion and Arithmetic Brownian Motion

A type of optimal investment problem can be regarded as an optimal stopping problem in the field of applied stochastic analysis. This study derives the existence conditions of the optimal stopping time when the stochastic process is a geometric Brownian motion or an arithmetic Brownian motion. The conditions concern the intrinsic value function and are natural extensions of the certainty case. ...

The Patched Brownian Motion Distribution

Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries

‎In this paper Lie symmetry analysis is applied to find new‎ solution for Fokker Plank equation of geometric Brownian motion‎. This analysis classifies the solution format of the Fokker Plank‎ ‎equation‎.

Motion by stopping: rectifying Brownian motion of nonspherical particles.

We show that Brownian motion is spatially not symmetric for mesoscopic particles embedded in a fluid if the particle is not in thermal equilibrium and its shape is not spherical. In view of applications to molecular motors in biological cells, we sustain nonequilibrium by stopping a nonspherical particle at periodic sites along a filament. Molecular dynamics simulations in a Lennard-Jones fluid...

Brownian Motion and the Generalized Catalan Numbers

We show that the generating functions of the generalized Catalan numbers can be identified with the moment generating functions of probability density functions related to the Brownian motion stochastic process. Specifically, the probability density functions are exponential mixtures of inverse Gaussian (EMIG) probability density functions, which arise as the first passage time distributions to...