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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 517.596
G.M. Perun,1 V.K. Yasinsky2

STOCHASTIC m -POINT CAUCHY PROBLEM OF PARABOLIC TYPE
WITH SEMIDIFFUSION PERTURBATIONS

Abstract. The problem of the existence, with probability 1, of Green’s function of a stochastic m -point Cauchy problem for a higher-order parabolic equation with white noise perturbations taken only with negative values is considered. Estimates are obtained in spaces of functions whose norm contains the mathematical expectation.

Keywords: m -point Cauchy problem, existence with probability 1, Ito’s formula, Green’s function, parabolicity condition, mathematical expectation.



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1 Yu. Fedkovych Chernivtsi National University, Chernivtsi, Ukraine,
e-mail: perungm@ukr.net.

2 Yu. Fedkovych Chernivtsi National University, Chernivtsi, Ukraine.

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