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Title: Finite-Dimensional Representations for Controlled Diffusions with Delay

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.
Authors:
 [1] ;  [2]
  1. Università di Milano, Dipartimento di Economia, Management e Metodi Quantitativi (Italy)
  2. Université Paris Diderot, Laboratoire de Probabilités et Modèles Aléatoires (France)
Publication Date:
OSTI Identifier:
22470059
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 71; Journal Issue: 1; Other Information: Copyright (c) 2015 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; DIFFERENTIAL EQUATIONS; DIFFUSION; ERRORS; MARKOV PROCESS; MATHEMATICAL SOLUTIONS; OPTIMAL CONTROL