An Introduction to Probability and Stochastic Processes |
Contents
Discrete Random Variables | 3 |
Absolutely Continuous Random Variables | 13 |
Distribution Functions | 22 |
Copyright | |
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A₁ absolutely continuous affine transformation aperiodic b₁ birth and death Borel bounded characteristic function choose compute condition convergence convex countably defined denote the number discrete density Dominated Convergence Theorem E(YX equation event exists a.s. exponentially distributed F(ax Find finite expectation follows fx(x fxy(x given Hoel holds i.i.d. sequence independent inequality integral invariant Karlin and Taylor Large Numbers Law of Large Lemma linear Markov chain matrix n₁ nonnegative Observe P₁ particles Parzen 45 Poisson process Port and Stone PROOF Px(x Pxy(t queue random affine transformation S₁ satisfies stationary distribution Stochastic Processes Stone 28 Subadditive Ergodic Theorem subset Suppose t₁ Taylor 31 transient transition probabilities unique vector X}nzo X₁ Xn+1 σ²