Some applications of Girsanov's theorem to the theory of stochastic differential inclusions

Micha Kisielewicz

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2003)

  • Volume: 23, Issue: 1, page 21-29
  • ISSN: 1509-9407

Abstract

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The Girsanov's theorem is useful as well in the general theory of stochastic analysis as well in its applications. We show here that it can be also applied to the theory of stochastic differential inclusions. In particular, we obtain some special properties of sets of weak solutions to some type of these inclusions.

How to cite

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Micha Kisielewicz. "Some applications of Girsanov's theorem to the theory of stochastic differential inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 23.1 (2003): 21-29. <http://eudml.org/doc/271455>.

@article{MichaKisielewicz2003,
abstract = {The Girsanov's theorem is useful as well in the general theory of stochastic analysis as well in its applications. We show here that it can be also applied to the theory of stochastic differential inclusions. In particular, we obtain some special properties of sets of weak solutions to some type of these inclusions.},
author = {Micha Kisielewicz},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {stochastic process; Girsanov’s theorem; stochastic differential inclusion; weak solution; Brownian motion; existence theorem; convexity},
language = {eng},
number = {1},
pages = {21-29},
title = {Some applications of Girsanov's theorem to the theory of stochastic differential inclusions},
url = {http://eudml.org/doc/271455},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Micha Kisielewicz
TI - Some applications of Girsanov's theorem to the theory of stochastic differential inclusions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2003
VL - 23
IS - 1
SP - 21
EP - 29
AB - The Girsanov's theorem is useful as well in the general theory of stochastic analysis as well in its applications. We show here that it can be also applied to the theory of stochastic differential inclusions. In particular, we obtain some special properties of sets of weak solutions to some type of these inclusions.
LA - eng
KW - stochastic process; Girsanov’s theorem; stochastic differential inclusion; weak solution; Brownian motion; existence theorem; convexity
UR - http://eudml.org/doc/271455
ER -

References

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  1. [1] F. Hiai, Multivalued stochastic integrals and stochastic inclusions, not published. 
  2. [2] M. Kisielewicz, Set-valued stochastic integral and stochastic inclusions, Stoch. Anal. Appl. 15 (5) (1997), 783-800. Zbl0891.93070
  3. [3] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ. Dordrecht, Boston, London 1991. Zbl0731.49001
  4. [4] B. Øksendal, Stochastic Differential Equations, Springer Verlag, Berlin, Heildelberg 1998. 
  5. [5] Ph. Proter, Stochastic Integration and Differential Equations, Springer Verlag, Berlin, Heidelberg 1990. 

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