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Deterministic optimal policies for Markov control processes with pathwise constraints

Armando F. Mendoza-Pérez, Onésimo Hernández-Lerma (2012)

Applicationes Mathematicae

This paper deals with discrete-time Markov control processes in Borel spaces with unbounded rewards. Under suitable hypotheses, we show that a randomized stationary policy is optimal for a certain expected constrained problem (ECP) if and only if it is optimal for the corresponding pathwise constrained problem (pathwise CP). Moreover, we show that a certain parametric family of unconstrained optimality equations yields convergence properties that lead to an approximation scheme which allows us to...

Directed forests with application to algorithms related to Markov chains

Piotr Pokarowski (1999)

Applicationes Mathematicae

This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.

Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings

Satoshi Ishiwata (2007)

Annales mathématiques Blaise Pascal

We obtain another proof of a Gaussian upper estimate for a gradient of the heat kernel on cofinite covering graphs whose covering transformation group has a polynomial volume growth. It is proved by using the temporal regularity of the discrete heat kernel obtained by Blunck [2] and Christ [3] along with the arguments of Dungey [7] on covering manifolds.

Dynamic programming for an investment/consumption problem in illiquid markets with regime-switching

Paul Gassiat, Fausto Gozzi, Huyên Pham (2015)

Banach Center Publications

We consider an illiquid financial market with different regimes modeled by a continuous time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a Cox process with intensity depending on the market regime. Moreover, the risky asset price is subject to liquidity shocks, which change its rate of return and volatility, and induce jumps on its dynamics. In this setting, we study the problem of an economic agent optimizing her expected utility from consumption...

Dynamiques recuites de type Feynman-Kac : résultats précis et conjectures

Pierre Del Moral, Laurent Miclo (2006)

ESAIM: Probability and Statistics

Soit U une fonction définie sur un ensemble fini E muni d'un noyau markovien irréductible M. L'objectif du papier est de comparer théoriquement deux procédures stochastiques de minimisation globale de U : le recuit simulé et un algorithme génétique. Pour ceci on se placera dans la situation idéalisée d'une infinité de particules disponibles et nous ferons une hypothèse commode d'existence de suffisamment de symétries du cadre (E,M,U). On verra notamment que contrairement au recuit simulé, toute...

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