A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans.
Name
671248552-MIT.pdf
Description
Full printable version
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5.82 MB
Format
Adobe PDF
Checksum (MD5)
0d1c5a492ad4d096b349c5c7ebcd6d9f
Author(s)
Evans, Lawrence C., 1949-
Advisor(s)
Daniel W. Stroock.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
This thesis consists of two results. The first result is a strong maximum principle for certain parabolic systems of equations, which, for illustrative purposes, I consider as reaction-diffusion systems. Using the theory of viscosity solutions, I give a proof which extends the previous theorem to no longer require any regularity assumptions on the boundary of the convex set in which the system takes its values. The second result is an approximation scheme for reflected stochastic differential equations (SDE) of the Stratonovich type. This is a joint result with Professor Daniel W. Stroock. We show that the distribution of the solution to such a reflected SDE is the weak limit of the distribution of the solutions of the reflected SDEs one gets by replacing the driving Brownian motion by its N-dyadic linear interpolation. In particular, we can infer geometric properties of the solutions to a Stratonovich reflected SDE from those of the solutions to the approximating reflected SDE.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 125-126).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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