Set-valued Stratonovich integral

Anna Góralczyk; Jerzy Motyl

Discussiones Mathematicae Probability and Statistics (2006)

  • Volume: 26, Issue: 1, page 63-81
  • ISSN: 1509-9423

Abstract

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The purpose of the paper is to introduce a set-valued Stratonovich integral driven by a one-dimensional Brownian motion. We discuss the existence of this integral and investigate its properties.

How to cite

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Anna Góralczyk, and Jerzy Motyl. "Set-valued Stratonovich integral." Discussiones Mathematicae Probability and Statistics 26.1 (2006): 63-81. <http://eudml.org/doc/277051>.

@article{AnnaGóralczyk2006,
abstract = {The purpose of the paper is to introduce a set-valued Stratonovich integral driven by a one-dimensional Brownian motion. We discuss the existence of this integral and investigate its properties.},
author = {Anna Góralczyk, Jerzy Motyl},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {set-valued function; Hukuhara differential; selection of a set-valued map; semimartingale; Stratonovich integral},
language = {eng},
number = {1},
pages = {63-81},
title = {Set-valued Stratonovich integral},
url = {http://eudml.org/doc/277051},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Anna Góralczyk
AU - Jerzy Motyl
TI - Set-valued Stratonovich integral
JO - Discussiones Mathematicae Probability and Statistics
PY - 2006
VL - 26
IS - 1
SP - 63
EP - 81
AB - The purpose of the paper is to introduce a set-valued Stratonovich integral driven by a one-dimensional Brownian motion. We discuss the existence of this integral and investigate its properties.
LA - eng
KW - set-valued function; Hukuhara differential; selection of a set-valued map; semimartingale; Stratonovich integral
UR - http://eudml.org/doc/277051
ER -

References

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  9. [9] M. Kisielewicz, M. Michta and J. Motyl, Set-valued approach to stochastic control. Existence and regularity properties, Dynamic Syst. Appl. 12 (3-4) (2003), 405-432. Zbl1063.93047
  10. [10] M. Kisielewicz, M. Michta and J. Motyl, Set-valued approach to stochastic control. Viability and semimartingale issues, Dynamic Syst. Appl. 12 (3-4) (2003), 433-466. Zbl1064.93042
  11. [11] V. Lakshmikhantam, T. Gnana Bhaskar and D. Vasundhara, Theory of Set Differential Equations in Metric Space, (preprint) (2004). 
  12. [12] P. Protter, Stochastic Integration and Differential Equations: A New Approach, Springer, New York 1990. 
  13. [13] J. San Martin, One-dimensional Stratonovich differential equations, Ann. Probab. 21 (1) (1993), 509-553. Zbl0773.60049
  14. [14] E. Wong and M. Zakai, On the convergence of ordinary integrals to stochastic integrals, Ann. Math. Statist. 36 (1965), 1560-1564. Zbl0138.11201

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