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MSC 60H30, 34K50, 34M99
Stochastic Leontiff–tupe equations with multiplicative effect in spase of complex–valued «noises»
Alexander Leonidovich Shestakov, South Ural State University (national research University), Chelyabinsk, Rector,
Minzilya Almasovna Sagadeeva , South Ural State University (national research University), Chelyabinsk, Assistant Professor,
We consider a Leontieff–type stochastic equation, that is, a system of differential equations implicit with respect to the time derivative in the spaces of random processes. The concepts previously introduced for the spaces of differentiable "noise" using the Nelson-Gliklikh derivative carry over to the case of complex–valued "noise"; in addition, the right-hand side of the equation is subject to multiplicative effect of a special form. We construct a solution to the Showalter-Sidorov problem for Leontieff-type equations with multiplicative effect of a complex–valued process of special form. Aside from the introduction and references, the article consists of two parts. In the first part we carry over various concepts of the space of real-valued differentiable "noise" to the complex–valued case. In the second part we construct a Showalter-Sidorov solution to a Leontieff-type equation with multiplicative effect of a complex-valued process of special form. The list of references is not intended to be complete and reflects only the authors' personal preferences.
Leontieff–type equations, multiplicative effect, Wiener process, Nelson–Gliklikh derivative, space of complex–valued "noises", "white noise"
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