Generalized Shapiro-Loginov formula and the moment stability of a string equation with the random telegraphic parameter

Od Vol. 53, issue 4/5 (2001) wyd: PAS. IFTR

The results concerning the moments of stochastic linear differential equations with the multiplicative parameter in the form of a stochastic telegraph process (Shapiro-Loginov formula) are generalized to the case of Hilbert-space-valued evolution equations. The obtained results are then applied to the investigation of the moment stability of some string equation with stochastic parametric excitation. The results obtained for exact and modal approaches are compared showing the possibility of the simplified analysis as well as differences. Additionally, the system with the appropriate white-noise excitation is considered, and, with the aid of an “equivalent” white-noise process the conditions of an approximation of the telegraphic stochastic process are studied.

[1], 141-435 s. ; 24 cm

Od Vol. 43, issue 1 (1991) wyd.: Polish Scientific Publishers = PWN

Od Vol. 50, issue 4 (1998) wyd.: Agencja Reklamowo-Wydawnicza A. Grzegorczyk