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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.
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| 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 |
| Source Type: | DISSERTATION |
| Subjects: | Mathematics |
| Keywords: | Intersection local times, Symmetric stable processes, Triple intersection local times |
| Publication Number: | 3553043 |
| ISBN: | 978-1-267-92244-1 |
