A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
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| Formato: | Tese |
| Idioma: | eng |
| Publicado em: |
Massachusetts Institute of Technology
2010
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| Acesso em linha: | http://hdl.handle.net/1721.1/59784 |
| _version_ | 1826195009305575424 |
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| author | Evans, Lawrence C., 1949- |
| author2 | Daniel W. Stroock. |
| author_facet | Daniel W. Stroock. Evans, Lawrence C., 1949- |
| author_sort | Evans, Lawrence C., 1949- |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. |
| first_indexed | 2024-09-23T10:05:39Z |
| format | Thesis |
| id | mit-1721.1/59784 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T10:05:39Z |
| publishDate | 2010 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/597842019-04-11T01:13:06Z A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans. Evans, Lawrence C., 1949- Daniel W. Stroock. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. Cataloged from PDF version of thesis. Includes bibliographical references (p. 125-126). 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. Ph.D. 2010-10-29T18:39:16Z 2010-10-29T18:39:16Z 2010 2010 Thesis http://hdl.handle.net/1721.1/59784 671248552 eng 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 126 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Evans, Lawrence C., 1949- A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans. |
| title | A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans. |
| title_full | A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans. |
| title_fullStr | A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans. |
| title_full_unstemmed | A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans. |
| title_short | A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans. |
| title_sort | strong maximum principle for reaction diffusion systems and a weak convergence scheme for reflected stochastic differential equations by lawrence christopher evans |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/59784 |
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