Preliminary knowledge 0.1 Probability spaces and random variables (elements) 0.2 Expectation and conditional expectation 0.3 Convergence and weak convergence 0.4 Martingale 0.5 Slowly varing function 0.6 The laws of large numbers 0.7 The central limit theorems 0.8 Branching process in a random environment 0.9 Multiplicative cascades in a random environment 0.10 Directed polymers in a random environment C.C.for R.W.S.of T.A.of B-valued M 1.1 Main resnlt 1.2 Preliminaries 1.3 Proof of the main result C.M.C.for R.W.S.of T.A.of B-valued M 2.1 Main results 2.2 Preliminaries 2.3 Proofs of the main results B 3.1 Some preliminary results 3.2 An equivalent of log m(n) 3.3 An equivalent of log M(n) 3.4 A sufficient condition for no exceptional point M 4.1 Central limit theorem 4.2 Convergence in L 4.3 Proof of Theorem 4 4.4 The Mandelbrot measures for M D 5.1 Main result 5.2 Proof of the main result 5.3 Proof of Corollary 5 Bibliography Index
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