# Strong and weak solutions to stochastic inclusions

Banach Center Publications (1995)

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

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topKisielewicz, 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

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

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