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