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Probability,

Random Processes,

and Ergodic Properties

November 3, 2001

ii

Probability,

Random Processes,

and Ergodic Properties

Robert M. Gray

Information Systems Laboratory

Department of Electrical Engineering

Stanford University

iv

°

1987 by Springer Verlag, 2001 revision by Robert M. Gray.

c

v

This book is a®ectionately dedicated to

Elizabeth Dubois Jordan Gray

and to the memory of

R. Adm. Augustine Heard Gray, U.S.N.

1888-1981

Sara Jean Dubois

and

William \Billy" Gray

1750-1825