Stationary distributions of the simplest dynamical systems in Rn perturbed by generalized Poisson process

Let z(t) [set membership, variant] Rn be a generalized Poisson process with parameter [lambda] and let A: Rn --> Rn be a linear operator. The conditions of existence and limiting properties as [lambda] --> [infinity] or as [lambda] --> 0 of the stationary distribution of the process x(t) [set membership, variant] Rn which satisfies the equation dx(t) = Ax(t)dt + dz(t) are investigated.