Note on the selection properties of set-valued semimartingales

Mariusz Michta

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1996)

  • Volume: 16, Issue: 2, page 161-169
  • ISSN: 1509-9407

Abstract

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Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.

How to cite

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Mariusz Michta. "Note on the selection properties of set-valued semimartingales." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 16.2 (1996): 161-169. <http://eudml.org/doc/275908>.

@article{MariuszMichta1996,
abstract = {Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.},
author = {Mariusz Michta},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {set-valued stochastic processes; conditional expectation; martingales; selections},
language = {eng},
number = {2},
pages = {161-169},
title = {Note on the selection properties of set-valued semimartingales},
url = {http://eudml.org/doc/275908},
volume = {16},
year = {1996},
}

TY - JOUR
AU - Mariusz Michta
TI - Note on the selection properties of set-valued semimartingales
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1996
VL - 16
IS - 2
SP - 161
EP - 169
AB - Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.
LA - eng
KW - set-valued stochastic processes; conditional expectation; martingales; selections
UR - http://eudml.org/doc/275908
ER -

References

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  1. [1] J.P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhauser, Boston 1990. 
  2. [2] G. Bocsan, On Wiener stochastic integral of a multifunction, Seminarul de Teoria Probabilitatilor si Applicatii, Univ. Timisoara 1987. 
  3. [3] H. Hess, On multivalued martingales whose values may be unbounded: martingale selectors and Mosco convergence, J. Multivar. Anal. 39 (1991), 175-201. Zbl0746.60051
  4. [4] F. Hiai, Multivalued stochastic integrals and stochastic differential inclusions, Division of Applied Mathematics, Research Institute of Applied Electricity, Sapporo 060, Japan, (preprint). 
  5. [5] F. Hiai, H. Umegaki, Integrals,conditional expectations,and martingales of multivalued functions, J. Multivar. Anal. 7 (1977), 149-182. Zbl0368.60006
  6. [6] M. Kisielewicz, Properties of solution set of stochastic inclusion, J. Appl. Math. Stoch. Anal. III, 6 (1993). 
  7. [7] M. Kisielewicz, Set-valued stochastic integrals and stochastic inclusions, Stoch. Anal. Appl. 16 (1) (1998) (in press). 
  8. [8] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer-PWN 1991. Zbl0731.49001
  9. [9] M. Kisielewicz, W. Sosulski, Set-valued stochastic integrals over martingale measures and stochastic inclusions, Discuss. Math., 15 (2) (1995), 179-188. Zbl0849.93058
  10. [10] M. Michta, L. Rybiński, Selections of set-valued stochastic processes, J. Appl. Math. Stoch. Anal. (in press). Zbl0910.60030
  11. [11] J. Motyl, Note on strong solutions of a stochastic inclusion, J. Appl. Math. Stoch. Anal. III 8 (1995), 291-297. Zbl0831.93061
  12. [12] N.S. Papageorgiou, On the theory of Banach space valued multifunctions, 1 Integration and conditional expectation, J. Multivar. Anal. 17 (1985), 185-206. Zbl0579.28009
  13. [13] P. Protter, Stochastic Integration and Differential Equations, Springer-Verlag 1990. Zbl0694.60047
  14. [14] K. Przesławski, Linear selectors and valuations for the family of compact and convex sets in Eucalideau vector space, Ph. D. Thesis, UAM, Poznań 1986. 
  15. [15] K. Przesławski, D. Yost, Lipschitz selections extentions and retractions, Quaderno 49 (1993), 1-18. 

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