Properties of set-valued stochastic integrals

Jerzy Motyl; Joachim Syga

Discussiones Mathematicae Probability and Statistics (2006)

  • Volume: 26, Issue: 1, page 83-103
  • ISSN: 1509-9423

Abstract

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We introduce set-valued stochastic integrals driven by a square-integrable martingale and by a semimartingale. We investigate properties of both integrals.

How to cite

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Jerzy Motyl, and Joachim Syga. "Properties of set-valued stochastic integrals." Discussiones Mathematicae Probability and Statistics 26.1 (2006): 83-103. <http://eudml.org/doc/277055>.

@article{JerzyMotyl2006,
abstract = {We introduce set-valued stochastic integrals driven by a square-integrable martingale and by a semimartingale. We investigate properties of both integrals.},
author = {Jerzy Motyl, Joachim Syga},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {decomposable set; Hausdorff metric; predictable set-valued process; square-integrable martingale; semimartingale},
language = {eng},
number = {1},
pages = {83-103},
title = {Properties of set-valued stochastic integrals},
url = {http://eudml.org/doc/277055},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Jerzy Motyl
AU - Joachim Syga
TI - Properties of set-valued stochastic integrals
JO - Discussiones Mathematicae Probability and Statistics
PY - 2006
VL - 26
IS - 1
SP - 83
EP - 103
AB - We introduce set-valued stochastic integrals driven by a square-integrable martingale and by a semimartingale. We investigate properties of both integrals.
LA - eng
KW - decomposable set; Hausdorff metric; predictable set-valued process; square-integrable martingale; semimartingale
UR - http://eudml.org/doc/277055
ER -

References

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  9. [9] I.I. Gihman and A.V. Skorohod, Stochastic Differential Equations, Springer Verlag, Berlin-Heidelberg-New York 1972. Zbl0242.60003
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  11. [11] F. Hiai, Multivalued stochastic integrals and stochastic differential inclusions, Division of Applied Mathematics, Research Institude of Applied Electricity, Sapporo 060, Japan, (not published). 
  12. [12] M. Kisielewicz, Set-valued Stochastic Integrals and Stochastic Inclusions, Stoch. Anal. Appl. 15 (5) (1997), 783-800. Zbl0891.93070
  13. [13] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ. and Polish Sci. Publ., Warszawa-Dordrecht-Boston-London 1991. Zbl0731.49001
  14. [14] M. Kisielewicz, M. Michta and J. Motyl, Set Valued Approach to Stochastic Control. Part I (Existence and regurality properties), Dynamic Syst. Appl. 12 (3) (2003), 405-432. Zbl1063.93047
  15. [15] M. Kisielewicz, M. Michta and J. Motyl, Set Valued Approach to Stochastic Control. Part II (Viability and Semimartingale Issues), Dynamic Syst. and Appl. 12 (3) (2003), 433-466. Zbl1064.93042
  16. [16] P. Protter, Stochastic Integration and Differential Equations (A New Approach), Springer-Verlag, Berlin-Heideberg-New York 1990. Zbl0694.60047

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