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Abstract: The general narrative of this work involves constructing the
time-changed Q-Wiener process and comparing it to the usual Q-Wiener process. Unlike its
non-time-changed counterpart, the time-changed Q-Wiener process lacks the nice properties
of having stationary and independent increments. Thus, we must turn to the martingale
property of the time-changed Q-Wiener process in order to ... read morerecover analogous results to the
ones known for the Q-Wiener process, without a time change. These results include
formulating stochastic differential equations (SDEs) driven by time-changed Q-Wiener
processes, establishing existence of solutions to these SDEs, exploring the stability of
those solutions, looking at associated Fokker-Planck-Kolmogorov equations, and making
connections to stochastic partial differential equations.
Thesis (Ph.D.)--Tufts University, 2016.
Submitted to the Dept. of Mathematics.
Advisor: Marjorie Hahn.
Committee: James Adler, Patricia Garmirian, and Sabir Umarov.
Keyword: Mathematics.read less