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Non-Smooth SDEs and Hyperbolic Lattice SPDEs Expansions via the Quadratic Covariation Differentiation Theory and Applications

Ashu, Tom A
http://rave.ohiolink.edu/etdc/view?acc_num=kent1500334062680747

Abstract Details

2017, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Using the Quadratic Covariation Differentiation (QCD) differentiation theory, we derive an infinite series non-smooth expansion of functions of solutions of Stochastic Differential Equations (SDE). We further derive the non-smooth QCD expansion explicitly in terms of the solution's transition density under additional smoothness conditions on the given SDE's drift and diffusion coefficients. We establish that, under certain smoothness conditions on the function acting on the SDE, our QCD expansion is the same as the Kloeden-Platen Stochastic Taylor Series expansion. We illustrate the applicability of these stochastic expansions with examples. We also extend our QCD expansion results from the SDE setting to the important hyperbolic Stochastic Partial Differential Equation (SPDE) setting with a non-smooth QCD representation and a non-smooth QCD expansion result for a rotated wave SPDE on the spatial lattice.
Hassan Allouba (Advisor)
Kazim Khan (Committee Member)
Gang Yu (Committee Member)
Austin Melton (Committee Member)
Mikhail Nesterenko (Committee Member)
69 p.
Applied Mathematics; Mathematics
Quadratic Covariation Differentiation; SDE; Stochastic Expansion; Stochastic Taylor Series Expansion; Kloeden and Platen; SPDE; Non smooth expansion; Stochastic Derivative; Ito Calculus Differentiation Theory; Functions of SDE; Functions of SPDE

Recommended Citations

Citations

  • Ashu, T. A. (2017). Non-Smooth SDEs and Hyperbolic Lattice SPDEs Expansions via the Quadratic Covariation Differentiation Theory and Applications [Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1500334062680747

    APA Style (7th edition)

  • Ashu, Tom. Non-Smooth SDEs and Hyperbolic Lattice SPDEs Expansions via the Quadratic Covariation Differentiation Theory and Applications. 2017. Kent State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1500334062680747.

    MLA Style (8th edition)

  • Ashu, Tom. "Non-Smooth SDEs and Hyperbolic Lattice SPDEs Expansions via the Quadratic Covariation Differentiation Theory and Applications." Doctoral dissertation, Kent State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1500334062680747

    Chicago Manual of Style (17th edition)

kent1500334062680747
297
© 2017, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.