Generalized grey Brownian motion local time: existence and weak approximation

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Strong Approximation of Brownian Motion

Simple random walk and Brownian motion are two strongly interconnected mathematical concepts. They are widely involved in not only pure math, but also in many other scientific fields. In this paper I will first introduce and define some basic concepts of discrete-time random walk. Then I will construct Brownian Motion with some basic properties, and use a method called the strong approximation ...

Large deviations for local time fractional Brownian motion and applications

Article history: Received 19 December 2007 Available online 9 June 2008 Submitted by M. Ledoux

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. ...

Local Time Flow Related to Skew Brownian Motion

We define a local time flow of skew Brownian motions, i.e., a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian motion. We prove several results on distributional and path properties of the flow. Our main result is a version of the RayKnight theorem on local times. In our case, however, t...