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Abstrakty
In this paper, we consider the following natural problem: suppose μ1 and μ2 are two probability measures with finite supports S(μ1), S(μ2) respectively, such that |S(μ1)| = |S(μ2)| and S(μ1) U S(μ2) ⊂ 2 × 2 stochastic matrices, and μn1 (the n-th convolution power of μ1 under matrix multiplication), as well as μn 2 , converges weakly to the same probability measure λ, where S(λ) ⊂ 2 × 2 stochastic matrices with rank one. Then when does it follow that μ1 = μ2? What if S(μ1) = S(μ2)? In other words, can two different random walks, in this context, have the same invariant probability measure? Here, we consider related problems.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
359--372
Opis fizyczny
Bibliogr. 3 poz.
Twórcy
autor
- Department of Mathematics, University of South Florida. Tampa, FL 33620-5700, U.S.A.
autor
- Department of Mathematics, University of South Florida. Tampa, FL 33620-5700, U.S.A.
Bibliografia
- [1] S. Dhar, A. Mukherjea and J. S. Ratti, A non-linear functional equation arising from convolution iterates of a probability measure on 2x2 stochastic matrices, J. Nonlinear Analysis 36 (2) (1999), pp. 151-176.
- [2] A. Mukherjea, Limit theorems: stochastic matrices, ergodic Markov chains, and measures on semigroups, in: Probabilistic Analysis and Related Topics, Vol. 2, Academic Press, 1979, pp. 143-203.
- [3] M. Rosenblatt, Markov Processes: Structure and Asymptotic Behavior, Springer, 1971.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f10c63b0-8c1f-4765-b612-cebf92e0f73c