Veretennikova, Maria (2014) Controlled continuous time random walks and their position dependent extensions. PhD thesis, University of Warwick.
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Abstract
Continuous Time Random Walks (CTRWs) are used widely for modelling anomalous diffusion. This thesis is the first research which focuses on optimal control of CTRWs, their modifications and their position dependent extensions. We derive the equation which may be called a fractional Hamilton Jacobi Bellman equation (FHJB), as it is similar to the HJB equation for controlled Markov processes. We present our original analysis of the FHJB equation, firstly working with its simpler linear version and obtaining useful regularity properties, and secondly, deriving the mild form of the FHJB, exploring its regularity properties and well-posedness. We present our novel theorems proving rigorous convergence for optimal payoffs of the scaled stochastic processes of our interest and give an interpretation of the solution of the FHJB equation as a solution to an optimization problem.
| Item Type: | Thesis [via Doctoral College] (PhD) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Library of Congress Subject Headings (LCSH): | Random walks (Mathematics), Differentiable dynamical systems |
| Official Date: | December 2014 |
| Dates: | Date Event December 2014 Submitted |
| Institution: | University of Warwick |
| Theses Department: | Mathematics Institute |
| Thesis Type: | PhD |
| Publication Status: | Unpublished |
| Supervisor(s)/Advisor: | Kolokoltsov, V. N. (Vasiliĭ Nikitich) |
| Sponsors: | Engineering and Physical Sciences Research Council, EP/HO23364/1 |
| Extent: | 2, 102 leaves |
| Language: | eng |
| URI: | https://wrap.warwick.ac.uk/66990/ |
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