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Bilinear random integrals

100%

Rosiński J.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS I. Introduction.....................................................................................................................................................................5 II. Preliminaries...................................................................................................................................................................7 1. Infinitely divisible probability measures on Banach spaces..........................................................................................7 2. Random measures......................................................................................................................................................9 III. Bilinear random integral...............................................................................................................................................11 1. Definition and necessary conditions for the existence of a random integral...............................................................11 2. Topology in the space of M-integrable functions........................................................................................................17 3. Characterization of M-integrable functions.................................................................................................................21 4. Approximation by simple functions and some contraction principles..........................................................................33 5. Stable symmetric random integrals............................................................................................................................42 IV. Random integrals of Banach space valued functions with respect to real valued random measures..........................45 1. Immediate corollaries from a general theory of random integrals and examples........................................................45 2. Gaussian and stable random integrals......................................................................................................................51 3. Comparison theorem and some applications.............................................................................................................62 References......................................................................................................................................................................70

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Generalized tempered stable processes

61%

Rosiński J., Sinclair J.

Banach Center Publications

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2010

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tom 90

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nr 1

153-170

EN

This work introduces the class of generalized tempered stable processes which encompass variations on tempered stable processes that have been introduced in the field, including "modified tempered stable processes", "layered stable processes", and "Lamperti stable processes". Short and long time behavior of GTS Lévy processes is characterized and the absolute continuity of GTS processes with respect to the underlying stable processes is established. Series representations of GTS Lévy processes are derived. Such representations can be used for simulation and illustration of GTS processes as well as for their theoretical study.

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On the space of vector-valued functions integrable with respect to the white noise

49%

Rosiński J., Suchanecki Z.

Colloquium Mathematicum

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1980

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tom 43

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nr 1

183-201

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Multilinear forms in Pareto-like random variables and product random measures

49%

Rosiński J., Woyczyński W. A.

Colloquium Mathematicum

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1987

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tom 51

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nr 1

303-313

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Limit theorems for randomly indexed sums of random vectors

36%

Rosiński J.

Colloquium Mathematicum

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1975-1976

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tom 34

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nr 1

91-107

Ograniczanie wyników

3 Colloquium Mathematicum

1 Banach Center Publications

5 Rosiński J.

1 Sinclair J.

1 Suchanecki Z.

1 Woyczyński W. A.

1 2010

2 1987

1 1980

1 1975

Bilinear random integrals

Generalized tempered stable processes

On the space of vector-valued functions integrable with respect to the white noise

Multilinear forms in Pareto-like random variables and product random measures

Limit theorems for randomly indexed sums of random vectors