Method of matrix continued fractions for the analysis of nonlinear stochastic systems

Spectral-correlation characteristics of the Brownian motion of inertial particles

“…which corresponds to stationary probability distribution (8). We introduce the dimensionless current time θ = ω 0 t and the corresponding time shift τ = ω 0 τ 1 .…”

“…(10). The even moments x 2n ≡ I n can be found by either numerical integration of the Boltzmann distribution or summation of the convergent continued fraction [8] …”

“…One-dimensional trinominal-interaction systems have solutions in the form of continued fractions, while the vector systems have solutions in the form of matrix continued fractions[8]. However, in this case, the equations for the desired moment functions upon the Laplace transform comprise the initial conditions as the free terms, and the trinominal form is violated.…”