منابع مشابه
On Measurable Stochastic Processes
In recent years probability theory has been formulated mathematically as measure theory; in the case of stochastic processes depending upon a continuous parameter the measures considered are defined on certain subspaces of the space of all functions of a real variable.! This formulation of stochastic processes depending upon a continuous parameter gives rise to certain measurability problems, a...
متن کاملOn Weakly Measurable Stochastic Processes and Absolutely Summing Operators
A linear and continuous operator between Banach spaces is said to be absolutely summing if it maps unconditionally convergent series into absolutely convergent series. Moreover, it improves properties of stochastic processes. Indeed, N.Ghoussoub in [7] proved that an operator is absolutely summing if and only if it maps amarts (asymptotic martingales) into uniform amarts. In this paper we go a ...
متن کاملBisimulation on Markov Processes over Arbitrary Measurable Spaces
We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates with a measurable space its collection of (sub)probability measures. This coalgebraic formulation allows one t...
متن کاملNotes on stochastic processes
A stochastic process is a type of mathematical object studied in mathematics, particularly in probability theory, which can be used to represent some type of random evolution or change of a system. There are many types of stochastic processes with applications in various fields outside of mathematics, including the physical sciences, social sciences, finance and economics as well as engineering...
متن کاملLectures on Stochastic Processes
3 4 CONTENTS 6 Markov chains: stationary distributions 35 6.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1940
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1940-0000918-4