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Journal of Applied Nonlinear Dynamics 6(1) (2017) 45--56 | DOI:10.5890/JAND.2017.03.004

M. Veretennikova$^{1}$; V. Kolokoltsov$^{2}$

$^{1}$ Department of Statistics and Data Analysis, National Research University Higher School of Economics, Moscow, Russia

$^{2}$ Department of Statistics, University of Warwick, Coventry, United Kingdom

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Abstract

In this paper we initiate the rigorous analysis of controlled Continuous Time Random Walks (CTRWs) and their scaling limits, which paves the way to the real application of the research on CTRWs, anomalous diffusion and related processes. For the first time the convergence is proved for payoff functions of controlled scaled CTRWs and their position dependent extensions to the solution of a new pseudodifferential equation which may be called the fractional Hamilton- Jacobi-Bellman equation.

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