ON THE MILD SOLUTIONS OF QUANTUM STOCHASTIC EVOLUTION INCLUSIONS

M. O. OGUNDIRAN

Title	ON THE MILD SOLUTIONS OF QUANTUM STOCHASTIC EVOLUTION INCLUSIONS
Publication Type	Journal Article
Year of Publication	2015
Authors	OGUNDIRAN, MO
Volume	19
Issue	2
Start Page	307
Pagination	12
Date Published	2015
ISSN	1083-2564
AMS	34A60, 81S25
Abstract	Under a Filippov-type assumption, a study of the Quantum stochastic evolution inclusions is done in this paper. Given a quantum stochastic evolution inclusions: $${ dx(t) ∈ Ax(t) + \int^t_0 K(t, s)(E(s, x(s))dΛ_π(s) + F(s, x(s))dA_f (s) }$$ $${ + G(s, x(s))dA^{+}_g (s) + H(s, x(s))ds) \ \ \ \ \ \ \ \ \ \ \ \ }$$ $${ x(t_0) = x_0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$$ where ${ A }$ is the infinitesimal generator of a ${ C_0 }$-semigroup of operators, ${ K }$ is a continuous function and ${ E, F, G, H }$ are Lipschitzian multivalued stochastic processes. We established the existence of mild solutions of the quantum stochastic evolution inclusions.
URL	http://www.acadsol.eu/en/articles/19/2/11.pdf
Refereed Designation	Refereed
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