# Set-valued random differential equations in Banach space

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

- Volume: 15, Issue: 2, page 191-200
- ISSN: 1509-9407

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topMariusz Michta. "Set-valued random differential equations in Banach space." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 15.2 (1995): 191-200. <http://eudml.org/doc/275974>.

@article{MariuszMichta1995,

abstract = {We consider the problem of the existence of solutions of the random set-valued equation:
(I) $D_HX_t = F(t,X_t)P.1$, t ∈ [0,T] -a.e.; X₀ = U p.1
where F and U are given random set-valued mappings with values in the space $K_c(E)$, of all nonempty, compact and convex subsets of the separable Banach space E. Under certain restrictions on F we obtain existence of solutions of the problem (I). The connections between solutions of (I) and solutions of random differential inclusions are investigated.},

author = {Mariusz Michta},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {set-valued mappings; Hukuchara's derivative; Aumann's integral; measurability of multifunctions; measurable selectors; set-valued mapping; random set-valued differential equation; Hukuchara derivative; set-valued stochastic process; random differential inclusion},

language = {eng},

number = {2},

pages = {191-200},

title = {Set-valued random differential equations in Banach space},

url = {http://eudml.org/doc/275974},

volume = {15},

year = {1995},

}

TY - JOUR

AU - Mariusz Michta

TI - Set-valued random differential equations in Banach space

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 1995

VL - 15

IS - 2

SP - 191

EP - 200

AB - We consider the problem of the existence of solutions of the random set-valued equation:
(I) $D_HX_t = F(t,X_t)P.1$, t ∈ [0,T] -a.e.; X₀ = U p.1
where F and U are given random set-valued mappings with values in the space $K_c(E)$, of all nonempty, compact and convex subsets of the separable Banach space E. Under certain restrictions on F we obtain existence of solutions of the problem (I). The connections between solutions of (I) and solutions of random differential inclusions are investigated.

LA - eng

KW - set-valued mappings; Hukuchara's derivative; Aumann's integral; measurability of multifunctions; measurable selectors; set-valued mapping; random set-valued differential equation; Hukuchara derivative; set-valued stochastic process; random differential inclusion

UR - http://eudml.org/doc/275974

ER -

## References

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- [12] M. Michta, Istnienie i jednoznaczność rozwiązań losowych równań różniczkowych o wielowartościowych, zwartych i wypukłych prawych stronach, Praca dokt. UAM Poznań, WSI Zielona Góra (1993).
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- [14] A. Tołstonogow, Differencjalnyje wkluczenija w Banachowych prostranstwach, Nauka 1986.

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