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Title: Controlled continuous time random walks and their position dependent extensions
Author: Veretennikova, Maria
ISNI:       0000 0004 5350 1108
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2014
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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.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EP/HO23364/1)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics