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 Jerome Griego
Third Committee Member
Rueben Hersh
Language
English
Document Type
Dissertation
Recommended Citation
Quiring, Donald. "Random Evolutions on Diffusion Processes." (1971). https://digitalrepository.unm.edu/math_etds/160
