Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Publicado
A completeness theorem for two-parameter stochastic processes
Palabras clave:
Theory of 2-parameter, Theory of stochastic, Martingales, Conditionally, Inconditionally, Probability logic (en)Descargas
Introduction: In this short note we are going to prove a completeness theorem for a logic that is adequate for the study of stochastic processes with 2-parameters, a result that can be seen as a natural step within the development of the so called probability logics. It builds on previous definitions and results of Keisler, [K1] and [K2], and in order to avoid repetitions we are going to assume the reader is already familiar with sections 1 and 2 from [K1], so that here we just limit ourselves to add whatever is needed to handle the new concepts. In this section we present the basic definitions of the theory of 2-parameter stochastic processes, pointing out its differences with the one parameter case. A good introduction to the general theory of 2-parameter is [W] together with the collection of articles in [KMS].
Referencias
[CW] CAIROLI, R. and WALSH, J., Stochastic Integrals in the plane. Acta Math. 134,1975.
[D] DALANG, R., On infinite perfect graphs and randomized stopping points on the plane, Prob. Theory and related fields 78, 1988.
[F1] FAJARDO, S., Completeness theorems for the general theory of processes. In Proc. sixth Latin American Logic symposium. LNM 1130, 1985.
[F2] FAJARDO, S., Probability Logic with conditional expectation. Annals Math. Logic 28, 1985.
[H] HOOVER, D., Probability Logic, Annals of Math. Logic, 286, 1984.
[HK] HOOVER, D. and KEISLER, H. J., Adapted Distributions, Trans. Amer. Math. Soc., 286, 1984.
[K1] KEISLER, H. J., A completeness proof for adapted probability logic. Annals of Pure and Applied Logic, 31, 198
[K2] KEISLER, H. J., Probability Quantifiers. In Model Theoretic Logics. Edited by Barwise, J. and Feferman, S. Springer Verlag, 1985.
[K3] KEISLER, H. J., Hyperfinite models of adapted probability logic. Ann. Pure and Applied Logic, 31, 1986.
[KMS] KOREZGLIOGLU, H., MAZZIOTO, G., and SZPIRGLAS, J. EDITORS "Processus aleatoires a deux indices", LNM 863, 1981.
[KS] KRENGEL, U. and SUCHESTON, L., Stopping rules and tactics for processes indexed by a direct set. Journal of multivariate Analysis 11, 1981.
[L] LOEVE, Probability Theory. D. van Nostrand, New York, 1955.
[W] WALSH, J., Martingales with a multidimensional pa rameter and stochastic integrals in the plane. In LNM 1215.
