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Information Journal Paper

Title

COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS

Pages

  173-183

Abstract

 Multivariate reward processes with reward functions of constant rates, defined  on a semi-Markov process, first were studied by Masuda and Sumita, 1991. Reward processes with nonlinear reward functions were introduced in Soltani, 1996. In this work we study a multivariate process s Z(t) = (Z1 (t),..., Z p (t)), t ≥ 0 , where Z1(t),...,Zp (t) are reward processes with nonlinear reward functions ρ1 ,...,ρ p respectively. The Laplace transform of the covariance matrix, Σ(t), is specified for given ρ1 ,...,ρ p , and if they are real analytic functions, then the covariance matrix is fully specified. This result in particular provides an explicit formula for the variances of univariate reward processes. We also view Σ(t) as a solution of a renewal equation.

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    APA: Copy

    KHOURSHIDIAN, K., & SOLTANI, A.R.. (2003). COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, 14(2), 173-183. SID. https://sid.ir/paper/529988/en

    Vancouver: Copy

    KHOURSHIDIAN K., SOLTANI A.R.. COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN[Internet]. 2003;14(2):173-183. Available from: https://sid.ir/paper/529988/en

    IEEE: Copy

    K. KHOURSHIDIAN, and A.R. SOLTANI, “COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS,” JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, vol. 14, no. 2, pp. 173–183, 2003, [Online]. Available: https://sid.ir/paper/529988/en

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