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Extra info for Probability in Banach Spaces II: Proceedings of the Second International Conference on Probability in Banach Spaces, 18–24 June 1978, Oberwolfach, Germany

Example text

Math. , 34, 329-333 (1963). [ii] J. Hajek, On linear statistical problems in stochastic processes, Czech. Math. , 87, 404-444 (1962). R. Baker, Mutual information, strong equivalence, and signal sample path properties for Gaussian processes, to appear, Information and Control. R. Baker, Capacity of the Gaussian channel without feedback, Information and Control, 37, 70-89 (1978). A CHARACTERIZATION OF ALMOST SURE CONVERGENCE A. Bellow 1 and A. A. Israel The paper is divided as follows: §i. Introduction.

The above definition of regular stopping time is standard in martin- gale theory (see [12], p. 73). We now give a llst of examples of abundant sets of stopping times that arise naturally in the literature. In fact each one of the sets in Examples i)- 5) below is abundant in the strict sense: i) S = [b and S = Tf. 2) The class of examples contained in Lem~a 3. , such that E(o) < +co. 4) The set S of all o C Tf satisfying the condition: P({~ > n}) = o(n). 2) The set S of all stopping times ~ ~ Tf that are regular for (X)n c N" 52 We now give some simple examples and counterexamples pertaining to sets of stopping times.

B. , Necessary and sufficient conditions for the uniform convergence of random trigonometric series, Lecture Note Series No. 50 (1978), Arhus University, Denmark. 32 I0. Marcus, M. B. , Random Fourier series on locally compact Abelian groups, Lecture Notes in Math° (Strasbourg seminar 1977-78). ii. Woyczynski, W. , Geometry and martingales in Banach spaces, Part II: Independent increments, Probability on Banach Space, Advances in Prob. 4 (1978), M. Decker, N. Y. , A note on the central limit theorem in Banach spaces, Ann.

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