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2 Demonstratio Mathematica

2 2001

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Remarks on the selfdecomposability and new examples

Jurek Z.

Demonstratio Mathematica

2001

Vol. 34, nr 2

241-250

The analytic property of the sel fdecomposability of characteristic functions is presented from stochastic processes point of view. This provides new examples or proofs, as well as a link between the stochastic analysis and the theory of characteristic functions. A new interpretation of the famous Levy's stochastic area formula is given.

Generalized translation operators and Markov processes

Thu N.

Demonstratio Mathematica

2001

Vol. 34, nr 2

295-304

We study the relationship between generalized translation operators and stochastic convolutions on locally compact spaces. We prove that stochastic convolution semigroups can generate Levy type processes which are strong Markov Feller processes and, as an example, we study the Bingham convolution and its dual on integers.