The Differentiability of Renormalized Triple Intersection Local Times

Title: The Differentiability of Renormalized Triple Intersection Local Times
Identifier: d_2009_2013:83f682f893fd:11645
identifier: 12276
Creator: Dhamoon, Subir Singh,
Contributor: Jay Rosen
Date: 2013
Language: English
Publisher: City University of New York.
Subject: Mathematics | Intersection Local Times | Renormalized Triple Intersection Local Times | Symmetric Stable Processes | Triple Intersection Local Times
Abstract: The evolution of the theory of triple intersection times over the past, approximately, two decades has centered primarily on two dimensional Brownian Motion and planar symmetric stable processes. The one dimensional cases have gone largely unstudied. In this thesis, we examine the differentiability of renormalized triple intersection local times for the two aforementioned Markov processes in R1. In more detail, we prove that the single partial derivative with respect to each spatial variable exists and show that each partial derivative is, in fact, jointly continuous in both space and time variables. During the course of our analysis, we discover that these results hold for the class of symmetric stable process for which 3/2 < beta < 2.
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics

Media: The Differentiability of Renormalized Triple Intersection Local Times