Strong and weak solutions to stochastic inclusions

Michał Kisielewicz

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 277-286
  • ISSN: 0137-6934

Abstract

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Existence of strong and weak 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 ∫ ℝ n H τ , z ( x τ ) q ( d τ , d z ) and x t - x s ∈ ∫ s t F τ ( x τ ) d τ + ∫ s t G τ ( x τ ) d w τ + ∫ s t ∫ | z | ≤ 1 H τ , z ( x τ ) q ( d τ , d z ) + ∫ s t ∫ | z | > 1 H τ , z ( x τ ) p ( d τ , d z ) , where p and q are certain random measures, is considered.

How to cite

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Kisielewicz, Michał. "Strong and weak solutions to stochastic inclusions." Banach Center Publications 32.1 (1995): 277-286. <http://eudml.org/doc/262679>.

@article{Kisielewicz1995,
abstract = {Existence of strong and weak solutions to stochastic inclusions $x_\{t\} - x_\{s\} ∈ ∫^\{t\}_\{s\} F_\{τ\}(x_\{τ\})dτ + ∫^\{t\}_\{s\} G_\{τ\}(x_\{τ\})dw_\{τ\} + ∫^\{t\}_\{s\} ∫_\{ℝ^\{n\}\} H_\{τ,z\}(x_\{τ\})q(dτ,dz)$ and $x_\{t\} - x_\{s\} ∈ ∫^\{t\}_\{s\} F_\{τ\}(x_\{τ\})dτ + ∫^\{t\}_\{s\}G_\{τ\}(x_\{τ\})dw_\{τ\} + ∫^\{t\}_\{s\}∫_\{|z|≤1\} H_\{τ,z\}(x_\{τ\})q(dτ,dz) + ∫^\{t\}_\{s\}∫_\{|z|>1\} H_\{τ,z\}(x_\{τ\})p(dτ,dz)$, where p and q are certain random measures, is considered.},
author = {Kisielewicz, Michał},
journal = {Banach Center Publications},
keywords = {strong and weak solutions; stochastic inclusions},
language = {eng},
number = {1},
pages = {277-286},
title = {Strong and weak solutions to stochastic inclusions},
url = {http://eudml.org/doc/262679},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Kisielewicz, Michał
TI - Strong and weak solutions to stochastic inclusions
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 277
EP - 286
AB - Existence of strong and weak solutions to stochastic inclusions $x_{t} - x_{s} ∈ ∫^{t}_{s} F_{τ}(x_{τ})dτ + ∫^{t}_{s} G_{τ}(x_{τ})dw_{τ} + ∫^{t}_{s} ∫_{ℝ^{n}} H_{τ,z}(x_{τ})q(dτ,dz)$ and $x_{t} - x_{s} ∈ ∫^{t}_{s} F_{τ}(x_{τ})dτ + ∫^{t}_{s}G_{τ}(x_{τ})dw_{τ} + ∫^{t}_{s}∫_{|z|≤1} H_{τ,z}(x_{τ})q(dτ,dz) + ∫^{t}_{s}∫_{|z|>1} H_{τ,z}(x_{τ})p(dτ,dz)$, where p and q are certain random measures, is considered.
LA - eng
KW - strong and weak solutions; stochastic inclusions
UR - http://eudml.org/doc/262679
ER -

References

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  1. [1] A. V. Skorohod, Studies in the Theory of Random Processes, Dover, New York, 1982. 
  2. [2] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ. and Polish Sci. Publ., Warszawa-Dordrecht, 1991. Zbl0731.49001
  3. [3] M. Kisielewicz, Properties of solution set of stochastic inclusions, J. Appl. Math. Stochastic Anal. 6 (1993), 217-236. Zbl0796.93106
  4. [4] M. Kisielewicz, Existence of strong solutions to stochastic inclusions, Discuss. Math. 15 (submitted). 
  5. [5] P. Protter, Stochastic Integration and Differential Equations, Springer, Berlin, 1990. 

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