UDC 519.21
1 Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine
 perungm@ukr.net
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THE CAUCHY PROBLEM FOR A STOCHASTIC PARABOLIC EQUATION
WITH A DEVIATION OF THE ARGUMENT
Abstract. The Cauchy problem for a stochastic nonlinear equation of parabolic type with delay is considered. Using Green’s function, a formula is derived for finding the solution of the problem by the method of steps. The existence of a solution is established with probability 1 and the solution is estimated according to a specially introduced norm.
Keywords: Cauchy problem, stochastic parabolic equation, method of steps, Fourier transform, Green’s function.
FULL TEXT
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