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

AbstractLet z(t) ∈ Rn be a generalized Poisson process with parameter λ and let A: Rn → Rn be a linear operator. The conditions of existence and limiting properties as λ → ∞ or as λ → 0 of the stationary distribution of the process x(t) ∈ Rn which satisfies the equation dx(t) = Ax(t)dt + dz(t) are investigated