Limiting-type theorem for conditional distributions of products of independent unimodular 2×2 matrices
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We consider a random process which is some version of the Brownian bridge in the space SL(2,R). Under simplifying assumptions we show that the increments of this process increase as √t as in the case of the usual Brownian motion in the Euclidean space. The main results describe the limiting distribution for properly normed increments.
KeywordsBrownian Motion Euclidean Space Random Process Conditional Distribution Brownian Bridge
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- 1.H. Fürstenberg,Noncommuting random products. Trans. Amer. Math. Soc.198, 3 (1963), 377–428.Google Scholar
- 2.V. N. Tutubalin,On limit theorems for the product of random matrices, Theory Prob. and Appl.10, 1 (1965), 15–27.Google Scholar
- 3.V. N. Tutubalin,Approximation of probability measures in variation and products of random matrices, Theory, Prob. and Appl.13, 1 (1968), 65–83.Google Scholar