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Law of total probability and Bayes' theorem in Riesz spaces
Liang Hong
This note generalizes the notion of conditional probability to Riesz spaces using the order-theoretic approach. With the aid of this concept, we establish the law of total probabil…
And-Douglas type characterization of generalized conditional expectations, optional projections and predictable projections
Liang Hong
Generalized conditional expectations, optional projections and predictable projections of stochastic processes play important roles in the general theory of stochastic processes, s…
The linear topology associated with weak convergence of probability measures
Liang Hong
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functi…
On the interpolation property and dominated decomposition property of quasimartingales
Liang Hong
For a quasimartingale majorized by another quasimartingale, it is natural to ask whether a third quasimartingale can be inserted between them. In this paper, we give an affirmative…
On the Riesz decomposition property and the interpolation property of stopping times
Liang Hong
It is known that random variables have the Riesz decomposition property and the interpolation property. These properties are not only interesting in their own rights; they have bee…