Masters Theses

Keywords and Phrases

Deep learning; numerical methods; stochastic differential equations

Abstract

"The curse of dimensionality is the non-linear growth in computing time as the dimension of a problem increases. Using the Deep Backwards Stochastic Differential Equation (Deep BSDE) method developed in [HJE18], I approximate the solution at an initial time to a one-dimensional diffusion equation. Although we only approximate a one-dimensional equation, this method extends well to higher dimensions because it overcomes the curse of dimensionality by evaluating the given partial differential equation along "random characteristics''. In addition to the implementation, I also present most of the mathematical theory needed to understand this method"-- Abstract, p. iii

Advisor(s)

Murphy, Jason

Committee Member(s)

Han, Daozhi
Zhang, Yanzhi

Department(s)

Mathematics and Statistics

Degree Name

M.S. in Applied Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Spring 2024

Pagination

vii, 67 pages

Note about bibliography

Includes_bibliographical_references_(pages 65-66)

Rights

© 2023 Daniel Gerlad Kovach II, All rights reserved

Document Type

Thesis - Open Access

File Type

text

Language

English

Thesis Number

T 12337

Electronic OCLC #

1427207621

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Mathematics Commons

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