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Dissertation Information for Thomas Simon Mountford

NAME:
- Thomas Simon Mountford

DEGREE:
- Ph.D.

DISCIPLINE:
- Statistics

SCHOOL:
- University of California, Berkeley (USA) (1986)

ADVISORS:
- None

COMMITTEE MEMBERS:
- None

MPACT Status: Incomplete - Not_Inspected

Title: ASPECTS OF BROWNIAN MOTION

Abstract: This thesis is concerned with the various aspects of Brownian motion. The first chapter deals with planar Brownian motion and was prompted by the papers of Lyons and McKean (1984) and Pitman and Yor (1986). The first section establishes that the process $\{(\theta\sp{a}, \theta\sp{b}): t \ge 0\}$ is transient, where $\theta\sp{a}$ and $\theta\sp{b}$ are the windings about two distinct points. In the next section, we make some general comments on a class of processes which generalize the above process. The succeeding section demonstrates a method of acquiring information about the homotopy word for planar Brownian motion in the twice punctured plane. We conclude the chapter with a result concerning the occupation of wedges by Brownian motion in a time neighbourhood of 0.

Chapters Two and Three arise from the papers of Rosen (1983), Rosen (1984) and German, Horowitz and Rosen (1984). These papers showed how theorems concerning general Gaussian processes could be used to recover classically obtained results as well as to give new information. We first show how Rosen's (1983) ideas settle an otherwise difficult problem. In the second section we examine the intersection process X(s,t) = B(t) $-$ B(s) for Brownian motion in four and higher dimensions. Our treatment owes much to the papers of Hawkes (1971, 1974 and 1977).

The thesis is concluded with Chapter Three in which we show how the approach of the three aforementioned papers can be used to extend a result of Kahane.

MPACT Scores for Thomas Simon Mountford

A = 0
C = 1
A+C = 1
T = 0
G = 0
W = 0
TD = 0
TA = 0
calculated 2008-01-31 06:14:48

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