## Introduction to the Theory of Random ProcessesAlthough there are many books available on the theory of random processes, there are few books featuring rigorous exposition that are suitable for elementary instruction. This is such a book. |

## Introduction to the Theory of Random ProcessesAlthough there are many books available on the theory of random processes, there are few books featuring rigorous exposition that are suitable for elementary instruction. This is such a book. |

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additive apply arbitrary assume basis belonging Borel bounded broad sense called Chapter characteristic function coincides completes the proof condition Consequently consider construct contains continuous converges corresponding countably covariance deﬁned deﬁnition denote derivatives determined differential distribution elements equal equation equivalent example exists expectation ﬁnite ﬁrst ﬁxed follows formula function f Furthermore given hence implies independent inequality instant integral interval jump Lemma limit linear Markov process mathematical matrix mean-square means measure metric necessary nonnegative o-algebra obtain operator positive probability problem process 5(t properties prove quantity random function random processes random variables relation REMARK representation respect sample functions satisﬁed satisfy Section separable sequence solution space spectral stationary stochastic subsets suﬂicient Suppose Theorem theory tion transform transition uniformly values vector virtue