On a multivariate storage process. (Ukrainian, English) Zbl 1097.60022

Zakusylo, O. K.; Lysak, N. P.

Teor. Jmovirn. Mat. Stat. 71, 72-81 (2004); translation in Theory Probab. Math. Stat. 71, 81-91 (2005).

The authors deal with the storage process \(x(t)\in R^{n}\) which satisfies the Langevin equation \(dx(t)=Ax(t)\,dt+dz(t)\), where \(z(t)\in R^{n}\) is a generalized Poisson process, in the case where the matrix \(A\) has a form \(A=UJU^{-1}\), \(J\) is a Jordan matrix, \(U\) is a non-singular matrix. The limit behaviour, as \(\lambda\to0\), of \(U^{-1}x(\cdot,\lambda)\) in the case where the distribution of \(x(\cdot,\lambda)\) is stationary, is studied.

Reviewer: A. D. Borisenko (Kyïv)

MSC:

60G10

Stationary stochastic processes

Keywords:

Langevin equation; generalized Poisson process; stationary distribution