Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 4: Biology and Problems of Health

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Table of Contents -- Front Matter(pp. i-x) -- Front Matter(pp. i-x) -- PREFACE(pp. xi-xiv) -- PREFACE(pp. xi-xiv) -- Table of Contents(pp. xv-xvi) -- Table of Contents(pp. xv-xvi) -- ACCESSIBLE TERMINAL TIMES(pp. 1-8) -- ACCESSIBLE TERMINAL TIMES(pp. 1-8) -- FIRST EXIT TIMES FROM A SQUARE ROOT BOUNDARY(pp. 9-16) -- FIRST EXIT TIMES FROM A SQUARE ROOT BOUNDARY(pp. 9-16) -- GENERAL LATERAL CONDITIONS FOR SOME DIFFUSION PROCESSES(pp. 17-50) -- GENERAL LATERAL CONDITIONS FOR SOME DIFFUSION PROCESSES(pp. 17-50) -- THE MARTIN BOUNDARY OF RECURRENT RANDOM WALKS ON COUNTABLE GROUPS(pp. 51-74) -- THE MARTIN BOUNDARY OF RECURRENT RANDOM WALKS ON COUNTABLE GROUPS(pp. 51-74) -- The author is obliged to Professor Spitzer for several discussions on the subject matter of this paper. -- An outline ... -- APPLICATION OF ADDITIVE FUNCTIONALS TO THE BOUNDARY PROBLEM OF MARKOV PROCESSES (LÉVY'S SYSTEM OF U-PROCESSES)(pp. 75-110) -- APPLICATION OF ADDITIVE FUNCTIONALS TO THE BOUNDARY PROBLEM OF MARKOV PROCESSES (LÉVY'S SYSTEM OF U-PROCESSES)(pp. 75-110) -- A SURVEY ON THE MARKOV PROCESS ON THE BOUNDARY OF MULTI-DIMENSIONAL DIFFUSION(pp. 111-130) -- A SURVEY ON THE MARKOV PROCESS ON THE BOUNDARY OF MULTI-DIMENSIONAL DIFFUSION(pp. 111-130) -- SOME THEOREMS CONCERNING RESOLVENTS OVER LOCALLY COMPACT SPACES(pp. 131-164) -- SOME THEOREMS CONCERNING RESOLVENTS OVER LOCALLY COMPACT SPACES(pp. 131-164) -- ON MARKOV GROUPS(pp. 165-174) -- ON MARKOV GROUPS(pp. 165-174) -- SOME PROBLEMS RELATING TO MARKOV GROUPS(pp. 175-186) -- SOME PROBLEMS RELATING TO MARKOV GROUPS(pp. 175-186) -- UNIFORM ERGODICITY IN MARKOV CHAINS(pp. 187-192) -- UNIFORM ERGODICITY IN MARKOV CHAINS(pp. 187-192) -- ON QUASI-COMPACT PSEUDO-RESOLVENTS(pp. 193-196) -- ON QUASI-COMPACT PSEUDO-RESOLVENTS(pp. 193-196) -- A NOTE ON MARKOV SEMIGROUPS WHICH ARE COMPACT FOR SOME BUT NOT ALL t > 0(pp. 197-200) -- A NOTE ON MARKOV SEMIGROUPS WHICH ARE COMPACT FOR SOME BUT NOT ALL t > 0(pp. 197-200) -- The following three statements are correct. -- (i) If, for some t > 0, Pt is quasi-compact, then it is quasi-compact for all t > 0. -- (ii) [(iii)] If, for some λ > 0, λRλ is compact [quasi-compact], then it is compact [quasi-compact] for all λ > 0. -- SOME LOCAL PROPERTIES OF MARKOV PROCESSES(pp. 201-212) -- SOME LOCAL PROPERTIES OF MARKOV PROCESSES(pp. 201-212) -- A LIMIT THEOREM FOR INDEPENDENT RANDOM VARIABLES(pp. 213-216) -- A LIMIT THEOREM FOR INDEPENDENT RANDOM VARIABLES(pp. 213-216) -- ON LOCAL AND RATIO LIMIT THEOREMS(pp. 217-224) -- ON LOCAL AND RATIO LIMIT THEOREMS(pp. 217-224) -- LIMITING DISTRIBUTIONS FOR BRANCHING PROCESSES(pp. 225-242) -- LIMITING DISTRIBUTIONS FOR BRANCHING PROCESSES(pp. 225-242) -- UNIQUENESS OF STATIONARY MEASURES FOR BRANCHING PROCESSES AND APPLICATIONS(pp. 243-254) -- UNIQUENESS OF STATIONARY MEASURES FOR BRANCHING PROCESSES AND APPLICATIONS(pp. 243-254) -- SOME PECULIAR SEMI-MARKOV PROCESSES(pp. 255-264) -- SOME PECULIAR SEMI-MARKOV PROCESSES(pp. 255-264) -- For the present note we shall suppose that we are given -- (i) the transition matrix ∥pij∥ of an irreducible and recurrent Markov chain of, possibly, infinitely many states; -- (ii) a sequence {Ωi(x)} of proper distribution functions of nonnegative random variables and such that there is at least one i such that Ωi,(0+) < 1. -- A THEOREM ON FUNCTIONS OF CHARACTERISTIC FUNCTIONS AND ITS APPLICATION TO SOME RENEWAL THEORETIC RANDOM WALK PROBLEMS(pp. 265-310) -- A THEOREM ON FUNCTIONS OF CHARACTERISTIC FUNCTIONS AND ITS APPLICATION TO SOME RENEWAL THEORETIC RANDOM WALK PROBLEMS(pp. 265-310) -- RENEWAL THEOREMS FOR MARKOV CHAINS(pp. 311-320) -- RENEWAL THEOREMS FOR MARKOV CHAINS(pp. 311-320) -- RANDOM MEASURE PRESERVING TRANSFORMATIONS(pp. 321-326) -- RANDOM MEASURE PRESERVING TRANSFORMATIONS(pp. 321-326) -- ROOTS OF THE ONE-SIDED N-SHIFT(pp. 327-334) -- ROOTS OF THE ONE-SIDED N-SHIFT(pp. 327-334) -- A GEOMETRIC CONSTRUCTION OF MEASURE PRESERVING TRANSFORMATIONS(pp. 335-360) -- A GEOMETRIC CONSTRUCTION OF MEASURE PRESERVING TRANSFORMATIONS(pp. 335-360) -- CONSERVATIVE POSITIVE CONTRACTIONS IN L¹(pp. 361-374) -- CONSERVATIVE POSITIVE CONTRACTIONS IN L¹(pp. 361-374) -- ON POINCARÉ'S RECURRENCE THEOREM(pp. 375-404) -- ON POINCARÉ'S RECURRENCE THEOREM(pp. 375-404) -- ERGODIC THEORY OF SHIFT TRANSFORMATIONS(pp. 405-414) -- ERGODIC THEORY OF SHIFT TRANSFORMATIONS(pp. 405-414) -- CLASSIFICATION OF STATES FOR OPERATORS(pp. 415-430) -- CLASSIFICATION OF STATES FOR OPERATORS(pp. 415-430) -- STRONG MIXING PROPERTIES OF MARKOV CHAINS WITH INFINITE INVARIANT MEASURE(pp. 431-446) -- STRONG MIXING PROPERTIES OF MARKOV CHAINS WITH INFINITE INVARIANT MEASURE(pp. 431-446) -- INVARIANT MEASURES ON PRODUCT SPACES(pp. 447-460) -- INVARIANT MEASURES ON PRODUCT SPACES(pp. 447-460) -- EXISTENCE OF BOUNDED INVARIANT MEASURES IN ERGODIC THEORY(pp. 461-472) -- EXISTENCE OF BOUNDED INVARIANT MEASURES IN ERGODIC THEORY(pp. 461-472) -- TRANSITION PROBABILITY OPERATORS(pp. 473-484) -- TRANSITION PROBABILITY OPERATORS.