NDLI: Convergence rates of Markov chain approximation methods for controlled diffusions with stopping

Content Provider	Springer Nature Link
Author	Song, Qingshuo Yin, Gang George
Copyright Year	2010
Abstract	This work is concerned with rates of convergence of numerical methods using Markov chain approximation for controlled diffusions with stopping (the first exit time from a bounded region). In lieu of considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations, a purely probabilistic approach is used. There is an added difficulty due to the boundary condition, which requires the continuity of the first exit time with respect to the discrete parameter. To prove the convergence of the algorithm by Markov chain approximation method, a tangency problem might arise. A common approach uses certain conditions to avoid the tangency problem. Here, by modifying the value function, it is demonstrated that the tangency problem will not arise in the sense of convergence in probability and in L $^{1}$. In addition, controlled diffusions with a discount factor is also treated.
Starting Page	600
Ending Page	621
Page Count	22
File Format	PDF
ISSN	10096124
Journal	Journal of Systems Science and Complexity
Volume Number	23
Issue Number	3
e-ISSN	15597067
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-07-06
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Controlled diffusion dynamic programming equation Markov chain approximation rate of convergence Statistics Statistical Physics, Dynamical Systems and Complexity Mathematics of Computing Operations Research/Decision Theory Systems Theory, Control
Content Type	Text
Resource Type	Article
Subject	Information Systems

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