Discrete probability measures on 2 × 2 stochastic matrices and a functional equation on [0, 1]

• Autorzy: Mukherjea A. , Ratti J. S.
• Języki publikacji: EN

Abstrakty

EN

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

EN

stochastic matrices; probability measure

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 2
• Strony: 359--372
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Mukherjea A.

• Department of Mathematics, University of South Florida. Tampa, FL 33620-5700, U.S.A.

autor

Ratti J. S.

• 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.