Applications of probability to partial differential equations and infinite dimensional analysis
Name
767740199-MIT.pdf
Description
Full printable version
Size
3.28 MB
Format
Adobe PDF
Checksum (MD5)
414eeba5e1cba8bba3c4c78eccf20ac8
Author(s)
Chen, Linan, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Daniel W. Stroock.
Date Issued
2011
Publisher
Massachusetts Institute of Technology
Abstract
This thesis consists of two parts. The first part applies a probabilistic approach to the study of the Wright-Fisher equation, an equation which is used to model demographic evolution in the presence of diffusion. The fundamental solution to the Wright-Fisher equation is carefully analyzed by relating it to the fundamental solution to a model equation which has the same degeneracy at one boundary. Estimates are given for short time behavior of the fundamental solution as well as its derivatives near the boundary. The second part studies the probabilistic extensions of the classical Cauchy functional equation for additive functions both in finite and infinite dimensions. The connection between additivity and linearity is explored under different circumstances, and the techniques developed in the process lead to results about the structure of abstract Wiener spaces. Both parts are joint work with Daniel W. Stroock.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 79-80).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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