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Convolution and limit theorems for conditionally free random variables. (English) Zbl 0874.60010
Summary: We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and from an analytic point of view, by presenting the basic formula for its \(R\)-transform. We calculate explicitly the distributions of the conditionally free Gaussian and conditionally free Poisson distribution.

MSC:
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60H99 Stochastic analysis
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