Conditions for convergence and rate of convergence of random series in \(K_\sigma\)-spaces of random variables. II. (English. Ukrainian original) Zbl 0940.60047

Kozachenko, Yu. V.

Theory Probab. Math. Stat. 57, 69-83 (1998); translation from Teor. Jmovirn. Mat. Stat. 57, 67-80 (1997).

[For part I see ibid. 56, 115-128 (1998) resp. ibid. 56, 112-125 (1997; Zbl 0923.60041).] The author studies the Karhunen-Loéve representation of stochastic processes with zero mean and continuous covariation function. Conditions of existence of solutions of the parabolic and the hyperbolic partial equations with random initial conditions from \(K_{\sigma}\)-spaces of random variables are investigated. Applications of the Fourier method to these equations are discussed and properties of their solutions are studied.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60G07	General theory of stochastic processes
60G10	Stationary stochastic processes
60G17	Sample path properties

Keywords:

Karhunen-Loéve representation; parabolic and hyperbolic equations; random initial conditions

Citations:

Zbl 0923.60041