# Set-valued Stratonovich integral

Discussiones Mathematicae Probability and Statistics (2006)

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

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topAnna 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] 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] 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] V. Lakshmikhantam, T. Gnana Bhaskar and D. Vasundhara, Theory of Set Differential Equations in Metric Space, (preprint) (2004).
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- [13] J. San Martin, One-dimensional Stratonovich differential equations, Ann. Probab. 21 (1) (1993), 509-553. Zbl0773.60049
- [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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