Set-valued stochastic integrals and stochastic inclusions in a plane

@article{WładysławSosulski2001,
abstract = {We present the concepts of set-valued stochastic integrals in a plane and prove the existence of a solution to stochastic integral inclusions of the form $z_\{s,t\} ∈ φ_\{s,t\} + ∫_\{0\}^\{s\} ∫_\{0\}^\{t\} F_\{u,v\}(z_\{u,v\})dudv + ∫_\{0\}^\{s\} ∫_\{0\}^\{t\}G_\{u,v\}(z_\{u,v\})dw_\{u,v\}$},
author = {Władysław Sosulski},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {stochastic inclusions in the plane; set-valued random field; two-parameter stochastic process; weak compactness; set-valued mapping; stochastic integral; stochastic inclusion; existence theorem; fixed point theorem; semi-continuity of the integrals; Michael's selection theorem},
language = {eng},
number = {2},
pages = {249-259},
title = {Set-valued stochastic integrals and stochastic inclusions in a plane},
url = {http://eudml.org/doc/271484},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Władysław Sosulski
TI - Set-valued stochastic integrals and stochastic inclusions in a plane
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2001
VL - 21
IS - 2
SP - 249
EP - 259
AB - We present the concepts of set-valued stochastic integrals in a plane and prove the existence of a solution to stochastic integral inclusions of the form $z_{s,t} ∈ φ_{s,t} + ∫_{0}^{s} ∫_{0}^{t} F_{u,v}(z_{u,v})dudv + ∫_{0}^{s} ∫_{0}^{t}G_{u,v}(z_{u,v})dw_{u,v}$
LA - eng
KW - stochastic inclusions in the plane; set-valued random field; two-parameter stochastic process; weak compactness; set-valued mapping; stochastic integral; stochastic inclusion; existence theorem; fixed point theorem; semi-continuity of the integrals; Michael's selection theorem
UR - http://eudml.org/doc/271484
ER -