Some results about randomized binary Markov chains: theory, computing and applications

ABSTRACT

This paper is addressed to give a generalization of the classical Markov methodology allowing the treatment of the entries of the transition matrix and initial condition as random variables instead of deterministic values lying in the interval $[0,1]$. This permits the computation of the first probability density function (1-PDF) of the solution stochastic process taking advantage of the so-called Random Variable Transformation technique. From the 1-PDF relevant probabilistic information about the evolution of Markov models can be calculated including all one-dimensional statistical moments. We are also interested in determining the computation of distribution of some important quantities related to randomized Markov chains (steady state, hitting times, etc.). All theoretical results are established under general assumptions and they are illustrated by modelling the spread of a technology using real data.

KEYWORDS:

• Randomized binary Markov chain
• random variable transformation technique
• first probability density function
• statistical moments
• mathematical modelling

2010 MSC SUBJECT CLASSIFICATION:

• 60J20
• 60J22
• 62E15

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

J.-C. Cortés http://orcid.org/0000-0002-6528-2155

A. Navarro-Quiles http://orcid.org/0000-0003-3800-072X

J.-V. Romero http://orcid.org/0000-0003-3366-6557

M.-D. Roselló http://orcid.org/0000-0002-5724-7683

Additional information

Funding

This work has been partially supported by the Ministerio de Economía y Competitividad [grant MTM2017-89664-P]. Ana Navarro Quiles acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigación y Desarrollo (PAID), Universitat Politècnica de València.