Viability theorems for stochastic inclusions

Michał Kisielewicz

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1995)

  • Volume: 15, Issue: 1, page 61-42
  • ISSN: 1509-9407

Abstract

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Sufficient conditions for the existence of solutions to stochastic inclusions x t - x s ∈ ∫ s t F τ ( x τ ) d τ + ∫ s t G τ ( x τ ) d w τ + ∫ s t ∫ I R ⁿ H τ , z ( x τ ) ν ̃ ( d τ , d z ) beloning to a given set K of n-dimensional cádlág processes are given.

How to cite

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Michał Kisielewicz. "Viability theorems for stochastic inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 15.1 (1995): 61-42. <http://eudml.org/doc/275850>.

@article{MichałKisielewicz1995,
abstract = {Sufficient conditions for the existence of solutions to stochastic inclusions $x_t - x_s ∈ ∫^t_s F_τ(x_τ)dτ + ∫^t_s G_τ(x_τ)dw_τ + ∫^t_s∫_\{IRⁿ\} H_\{τ,z\}(x_τ)ν̃ (dτ,dz)$ beloning to a given set K of n-dimensional cádlág processes are given.},
author = {Michał Kisielewicz},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {stochastic processes; stochastic inclusions; optimal control},
language = {eng},
number = {1},
pages = {61-42},
title = {Viability theorems for stochastic inclusions},
url = {http://eudml.org/doc/275850},
volume = {15},
year = {1995},
}

TY - JOUR
AU - Michał Kisielewicz
TI - Viability theorems for stochastic inclusions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1995
VL - 15
IS - 1
SP - 61
EP - 42
AB - Sufficient conditions for the existence of solutions to stochastic inclusions $x_t - x_s ∈ ∫^t_s F_τ(x_τ)dτ + ∫^t_s G_τ(x_τ)dw_τ + ∫^t_s∫_{IRⁿ} H_{τ,z}(x_τ)ν̃ (dτ,dz)$ beloning to a given set K of n-dimensional cádlág processes are given.
LA - eng
KW - stochastic processes; stochastic inclusions; optimal control
UR - http://eudml.org/doc/275850
ER -

References

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  1. [1] J. P. Aubin, and A. Cellina, Differential Inclusions, Springer-Verlag 1984. Zbl0538.34007
  2. [2] J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäser 1990. 
  3. [3] F. Hiai, and H. Umegaki, Integrals, conditional expections and martingals of multifunctions, J. Multivariate Anal. 7 (1977), 149-182. Zbl0368.60006
  4. [4] M. Kisielewicz, Set-valued stochastic integrals and stochastic inclusions, Journal of Stochastic Analysis and Applications (submitted to print). 
  5. [5] M. Kisielewicz, Properties of solution set of stochastic inclusions, Journal of Appl. Math. and Stochastic Analysis 6 (3) (1993), 217-236. Zbl0796.93106
  6. [6] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ. and Polish Sci. Publ. Warszawa - Dordrecht - Boston - London (1991). Zbl0731.49001
  7. [7] N. S. Papageorgiou, Decomposable sets in the Lebesgue-Bochner spaces, Comm. Math. Univ. Sancti Pauli 37 (1) (1988), 49-62. Zbl0679.46032
  8. [8] Ph. Protter, Stochastic Integration and Differential Equations, Springer-Verlag (1990), Berlin - Heildelberg - New York. 

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