Publication Date

Spring 1-6-1971

Abstract

Let {V(t,ω), t ≥ O, ω ε Ω} be a diffusion process on the real line with infinitesimal operator 1/2σ2(⋅)D2 + m(⋅)D. Markov processes {Vn, n = 1,2,....} on the real line are constructed in such a way that the paths of Vn are step functions with jump size n-1/2 and

PO [lim sup |Vn(s)-V(s)| = 0] =1

n∞ 0≤s≤t,

where PO assigns probability one to paths starting at the origin at t = 0.

Let {TV(t), t≥0, vε R} be a family of linear contraction operators on a Banach space B. Suppose TV(t)f is continuous in v for all t≥0, fεB, and TV(t)TW(s) = TW(s)TV(t) for all t,s≥0, v,wε R. Let AV be the infinitesimal operator of TV.

Abstract continued in dissertation.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

L. H. Koopmans

Second Committee Member

Richard Griego

Third Committee Member

Rueben Hersh

Document Type

Dissertation

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