A REPRESENTATION FOR CHARACTERISTIC FUNCTIONALS OF STABLE RANDOM MEASURES WITH VALUES IN SAZONOV SPACES

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MAHMOUDI S.; SOLTANI A.R.

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Journal: Bulletin of the Iranian Mathematical Society Year:2010 | Volume:36 | Issue:1 Page(s): 27-39

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Title

A REPRESENTATION FOR CHARACTERISTIC FUNCTIONALS OF STABLE RANDOM MEASURES WITH VALUES IN SAZONOV SPACES

Author(s)

MAHMOUDI S. | SOLTANI A.R. | Issue Writer Certificate

Keywords

SEPARABLE BANACH SPACE

SAZANOV SPACE

BANACH VALUED RANDOM VECTOR

BOCHNER INTEGRAL

STABLE RANDOM MEASURE

Abstract

We deal with a Sazonov space (X: real separable) valued symmetric alpha STABLE RANDOM MEASURE Phi with independent increments on the measurable space (R-k, B(R-k)). A pair (k, mu), called here a control pair, for which k : X x R-k -> R+, mu a positive measure on (R-k, B(R-k)), is introduced. It is proved that the law of Phi is governed by a control pair; and every control pair will induce such Phi. Moreover, k is unique for a given mu. Our derivations are based on the Generalized Bochner Theorem and the Radon-Nikodym Theorem for vector measures.

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APA: Copy

MAHMOUDI, S., & SOLTANI, A.R.. (2010). A REPRESENTATION FOR CHARACTERISTIC FUNCTIONALS OF STABLE RANDOM MEASURES WITH VALUES IN SAZONOV SPACES. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 36(1), 27-39. SID. https://sid.ir/paper/574751/en

Vancouver: Copy

MAHMOUDI S., SOLTANI A.R.. A REPRESENTATION FOR CHARACTERISTIC FUNCTIONALS OF STABLE RANDOM MEASURES WITH VALUES IN SAZONOV SPACES. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2010;36(1):27-39. Available from: https://sid.ir/paper/574751/en

IEEE: Copy

S. MAHMOUDI, and A.R. SOLTANI, “A REPRESENTATION FOR CHARACTERISTIC FUNCTIONALS OF STABLE RANDOM MEASURES WITH VALUES IN SAZONOV SPACES,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 36, no. 1, pp. 27–39, 2010, [Online]. Available: https://sid.ir/paper/574751/en

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