 | Högnäs G. Probability measures on semigroups: convolution products, random walks and random matrices / G.Högnäs, A.Mukherjea. - 2nd ed. - New York: Springer, 2011, xii, 430 p. - (Probability and its applications). - Ref.: p.413-422. - Ind.: p.423-430. - ISBN 978-0-387-77547-0; ISSN 1431-7028
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1 Semigroups ................................................... 1
1.1 Introduction ............................................ 1
1.2 Homomorphisms, Quotients, and Products .................. 6
1.3 Semigroups with Zero ................................... 10
1.4 The Rees-Suschkewitsch Representation Theorem .......... 12
1.5 Topological Semigroups ................................. 22
1.6 Semigroups of Matrices ................................. 33
1.7 Semigroups of Infinite Dimensional Matrices ............ 53
1.8 Notes and Comments ..................................... 60
2 Probability Measures on Topological Semigroups .............. 63
2.1 Introduction ........................................... 63
2.2 Invariant and Idempotent Probability Measures .......... 64
2.3 Weak Convergence of Convolution Products of
Probability Measures ................................... 83
2.4 Weak Convergence of Convolution Products of
Nonidentical Probability Measures ..................... 137
2.5 Notes and Comments .................................... 168
3 Random Walks on Semigroups ................................. 171
3.1 Introduction .......................................... 171
3.2 Discrete Semigroups ................................... 180
3.3 Locally Compact Groups ................................ 198
3.4 Compact Semigroups .................................... 219
3.5 Completely Simple Semigroups .......................... 241
3.6 Notes and Comments .................................... 247
4 Random Matrices ............................................ 253
4.1 Introduction .......................................... 253
4.2 Recurrent Random Walks in Nonnegative Matrices ........ 254
4.3 Tightness of Products of I.I.D. Random Matrices:
Weak Convergence ...................................... 284
4.4 Invariant Measures for Random Walks in Nonnegative
Matrices: Laws of Large Numbers ....................... 333
4.5 Notes and Commments ................................... 355
A Products of I.I.D. Random Stochastic Matrices: Their
Skeletons and Convergence in Distribution .................. 359
В An Example Due to Chamayou and Letac ....................... 365
С Asymptotic Behavior of ||XnXn-1 ... Х0u|| for I.I.D.
Random Nonnegative Matrices ................................ 369
D Continuous Singularity of the Limit Distribution of
Products of I.I.D. Stochastic Matrices ..................... 383
E Rate of Decay of Concentration Functions on Discrete
Groups, by T.M. Retzlaff ................................... 397
E.1 Preliminaries ......................................... 397
E.2 Irreducible Measures .................................. 404
E.3 Adapted Measures ...................................... 408
References ................................................. 413
Index ......................................................... 423
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