On stochastically differentiable stationary Gaussian processes. II. (Russian) Zbl 0581.60029

Ryzhov, Yu. M.

Teor. Veroyatn. Mat. Stat. 31, 126-133 (1984).

[For part I see ibid. 10, 139-153 (1974; Zbl 0331.60023).]
The paper contains some sufficient conditions under which a stationary Gaussian process \(\xi\) (t), \(t\in R^ 1\), is stochastically equivalent to the process \({\tilde \xi}(t)=\xi (0)+\int^{t}_{0}\eta (s)ds+\sigma dw(t),\) where \(\eta\) (t) is a stationary Gaussian process subordinated to \(\xi\) (t) and w(t) is a Brownian motion process. As a corollary, equivalence conditions for Gaussian measures corresponding to stationary random processes in \(R^ n\) are obtained.

MSC:

60G15	Gaussian processes
60G10	Stationary stochastic processes
60J65	Brownian motion

Keywords:

stationary Gaussian process; equivalence conditions for Gaussian measures

Citations:

Zbl 0331.60023