2026-09-19T04:05:10Zhttps://dspace.mit.edu/server/oai/request

oai:dspace.mit.edu:1721.1/597842022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022

Daniel W. Stroock. Evans, Lawrence C., 1949- Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Department of Mathematics 2010-10-29T18:39:16Z 2010-10-29T18:39:16Z 2010 2010 http://hdl.handle.net/1721.1/59784 671248552 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. 126 p. eng Massachusetts Institute of Technology 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 Mathematics. A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans. Thesis application/pdf Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="3b3c8b88-caa0-40a2-82ff-4138dc4e0838"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans.</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2010</PublicationDate> <Authors> <Author> <DisplayName>Evans, Lawrence C., 1949-</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Mathematics.</Keyword> <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.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>