Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 79-80). / 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. / by Linan Chen. / Ph.D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/67787 |
| Date | January 2011 |
| Creators | Chen, Linan, Ph. D. Massachusetts Institute of Technology |
| Contributors | Daniel W. Stroock., Massachusetts Institute of Technology. Dept. of Mathematics., Massachusetts Institute of Technology. Dept. of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 80 p., application/pdf |
| Rights | M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission., http://dspace.mit.edu/handle/1721.1/7582 |
Page generated in 0.0019 seconds