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Dissertation/Thesis Abstract

The Differentiability of Renormalized Triple Intersection Local Times
by Dhamoon, Subir Singh, Ph.D., City University of New York, 2013, 175; 3553043
Abstract (Summary)

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 < β < 2.


Indexing (document details)
Advisor: Rosen, Jay
Commitee: Kosygina, Elena, Marcus, Michael
School: City University of New York
Department: Mathematics
School Location: United States -- New York
Source: DAI-B 74/06(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Intersection local times, Symmetric stable processes, Triple intersection local times
Publication Number: 3553043
ISBN: 978-1-267-92244-1
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