Book Review: Discrete-time Markov control processes: Basic optimality criteria
نویسندگان
چکیده
منابع مشابه
Discrete-time Markov control processes with discounted unbounded costs: Optimality criteria
We consider discrete-time Markov control processes with Borel state and control spaces, unbounded costs per stage and not necessarily compact control constraint sets. The basic control problem we are concerned with is to minimize the infinite-horizon, expected total discounted cost. Under easily verifiable assumptions, we provide characterizations of the optimal cost function and optimal polici...
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In this paper, we study the nth-bias optimality problem for finite continuous-time Markov decision processes (MDPs) with a multichain structure. We first provide nth-bias difference formulas for two policies and present some interesting characterizations of an nth-bias optimal policy by using these difference formulas. Then, we prove the existence of an nth-bias optimal policy by using nth-bias...
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In this paper we consider a discrete scale invariant Markov process {X(t), t ∈ R} with scale l > 1. We consider to have some fix number of observations in every scale, say T , and to get our samples at discrete points α, k ∈ W, where α is obtained by the equality l = α and W = {0, 1, . . .}. So we provide a discrete time scale invariant Markov (DT-SIM) process X(·) with parameter space {α, k ∈ ...
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These are lecture notes for the class Stochastic Calculus offered at the Courant Institute in the Fall Semester of 2012. It is a graduate level class. Students should have a solid background in probability and linear algebra. The topic selection is guided in part by the needs of our MS program in Mathematics in Finance. But it is not focused entirely on the Black Scholes theory of derivative pr...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1997
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-97-00708-8