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Completeness theorems for the general theory of stochastic processes. (English) Zbl 0595.03014
Methods in mathematical logic, Proc. 6th Latin Amer. Symp., Caracas/Venez. 1983, Lect. Notes Math. 1130, 174-194 (1985).
[For the entire collection see Zbl 0556.00007.]
Stochastic processes are one of the main topics of probability theory. Many of the concepts in stochastic analysis could be naturally expressed in a language with integral quantifiers and conditional expectation operators. From these ideas probability logic began. Adapted probability logic is a logic adequate for the study of stochastic processes. In the paper the author shows how to axiomatize in this logic the basic notions of the theory of stochastic processes, that is, stopping time, martingale and so on, and proves a ”completeness” theorem for each of the studied notions.
Reviewer: D.Costatini

03B48 Probability and inductive logic
60G05 Foundations of stochastic processes
60A05 Axioms; other general questions in probability