Adapted integral representations of random variables

Adapted Integral Representations by Measures on Choquet Boundaries

A Class of Integral Operators Generated by Random Variables

Let X be a random variable in Rp distributed symmetrically about zero with cumulants of order 4, 8, 12, . . . equal to zero. This class of random variables includes the multivariate normal. Consider the linear integral operator KX defined by KX g(x) = E [g(x+X)] = ∫ g(x + y) dP (X ≤ y) acting on the space of functions g : Cp → Cq with Taylor series expansions about zero. By Fredholm theory, non...

On some expectation and derivative operators related to integral representations of random variables with respect to a PII process

Given a process with independent increments X (not necessarily a martingale) and a large class of square integrable r.v. H = f(XT ), f being the Fourier transform of a finite measure μ, we provide explicit Kunita-Watanabe and Föllmer-Schweizer decompositions. The representation is expressed by means of two significant maps: the expectation and derivative operators related to the characteristics...

On the Ratio of Rice Random Variables

 The ratio of independent random variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice random variables. Ratios of such random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) a...

Application of some integral transforms and multiple hypergeometric functions in modeling randomly weighted average of some random variables

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