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Transformations of Stochastic Orderings
1994Incomplete orderings of distributions are nowadays used routinely in the analysis of uncertainty, inequality, welfare and poverty. The popularity of these orderings - of which stochastic dominance and Lorenz dominance are the best known examples - is due to the fact that they distinguish those distributional rankings which are widely accepted from ...
Patrick Moyes, Anthony Shorrocks
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Stochastic path-ordered exponentials
Journal of Mathematical Physics, 1984We prove convergence of an approximation of the stochastic product integral for conditional Wiener paths to the solution of a certain stochastic integral equation. This is used to establish the Wiener–Itô representation for the kernel of the semigroup exp t ΔA, where ΔA =∑μ (∂μ1+Aμ)2 for functions Aμ with values in the space of anti-Hermitian matrices.
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Uniform conditional stochastic order
Journal of Applied Probability, 1980One probability measure is less than or equal to another in the sense of UCSO (uniform conditional stochastic order) if a standard form of stochastic order holds for each pair of conditional probability measures obtained by conditioning on appropriate subsets.
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