Forward and reverse representations for Markov chains

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type , Research , Preprint , Report 01 Aug 2007 Germany, Germany, Russian Federation English Publisher:Elsevier BVJournal:Stochastic Processes and their Applications, volume 117, pages 1,052-1,075 (issn: 0304-4149,

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Authors: Milstein, Grigori N.; Schoenmakers, John G. M.; Spokoiny, Vladimir;

doi: 10.1016/j.spa.2006.12.002 , 10.20347/wias.preprint.1125

handle: 10419/25122

Forward and reverse representations for Markov chains

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Abstract

In this paper we carry over the concept of reverse probabilistic representations developed in Milstein, Schoenmakers, Spokoiny (2004) for diffusion processes, to discrete time Markov chains. We outline the construction of reverse chains in several situations and apply this to processes which are connected with jump-diffusion models and finite state Markov chains. By combining forward and reverse representations we then construct transition density estimators for chains which have root-N accuracy in any dimension and consider some applications.

Countries

Germany, Germany, Russian Federation

Related Organizations

Humboldt-Universität zu Berlin
Germany
Weierstrass Institute for Applied Analysis and Stochastics
Germany
Humboldt-Universität zu Berlin
FEDERAL STATE AUTONOMOUS EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION NOTHERN (ARCTIC) FEDERAL UNIVERSITY
Russian Federation
Ural State Agrarian University
Russian Federation

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Keywords

FINITE AUTOMATA, Statistics and Probability, 65C05, estimation of risk -- transition density estimation -- forward and reverse Markov chains -- Monte Carlo simulation, COMPUTER SIMULATION, PARAMETER ESTIMATION, REVERSE ENGINEERING, transition density estimation, forward and reverse Markov chains, Monte Carlo simulation, estimation of risk, forward and reverse Markov chains, 17 Wirtschaft, FORWARD AND REVERSE MARKOV CHAINS, PROBABILISTIC LOGICS, 510, MONTE CARLO SIMULATION, DISCRETE TIME CONTROL SYSTEMS, 60J05, Modelling and Simulation, 62G07, RISK ASSESSMENT, MARKOV PROCESSES, Estimation of risk, Monte Carlo simulation, Transition density estimation, ddc:510, TRANSITION DENSITY ESTIMATION, estimation of risk, ddc:330, 330 Wirtschaft, Markov processes: estimation; hidden Markov models, Applied Mathematics, article, JUMP DIFFUSION MODELS, Monte Carlo methods, MONTE CARLO METHODS, Forward and reverse Markov chains, Markov chains (discrete-time Markov processes on discrete state spaces), Density estimation, transition density estimation, ESTIMATION OF RISK, 60H10, jel: jel:C13, jel: jel:C15

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