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A pseudo-Markov property for controlled diffusion processes

Claisse, Julien; Talay, Denis; Tan, Xiaolu (2016), A pseudo-Markov property for controlled diffusion processes, SIAM Journal on Control and Optimization, 54, 2, p. 1017-1029. 10.1137/151004252

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1501.03939v1
Date
2016
Journal name
SIAM Journal on Control and Optimization
Volume
54
Number
2
Publisher
SIAM - Society for Industrial and Applied Mathematics
Pages
1017-1029
Publication identifier
Metadata
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Author(s)
Claisse, Julien
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Talay, Denis
Inria Sophia Antipolis - Méditerranée [CRISAM]
Tan, Xiaolu
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this note, we propose two different approaches to rigorously justify a pseudo-Markov property for controlled diffusion processes which isoften (explicitly or im-plicitly) used to prove the dynamic programming principle in the stochastic controlliterature. The first approach develops a sketch of proof proposed by Fleming andSouganidis [9]. The second approach is based on an enlargement of the originalstate space and a controlled martingale problem. We clarifysome measurabilityand topological issues raised by these two approaches.
Subjects / Keywords
martingale problem; dynamic programming principle; Stochastic control; pseudo-Markov property