Non linear systems under complex α-stable Lèvy white noise

American Society of Mechanical Engineers, Applied Mechanics Division, AMD

Volumn 254, Issue , 2003, Pages 207-213

  Di Paola, M ^a,b   Vasta, M ^a,b  

^a UNIVERSITY OF PALERMO   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FOURIER TRANSFORMS; FUNCTIONS; IMPULSE NOISE; METHOD OF MOMENTS; PROBABILITY DENSITY FUNCTION; SET THEORY; WHITE NOISE;

POISSON WHITE NOISE; POISSONIAN PROCESSES;

NONLINEAR SYSTEMS;

EID: 1842583651     PISSN: 01608835     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/IMECE2003-55469     Document Type: Conference Paper

References (21)

1. Samorodnitsky, G. and Taqqu, M.S., " Stable non Gaussian random processes. Stochastic models with infinite variance" . Chapman and Hall, London, 1994.
2. West, B., Seshadri, V., " Linear systems under Lèvy fluctuations" , Phisica 113A, 203-216, 1982.
3. Grigoriu, M., " Linear systems subjected to non-Gaussian α-stable processes" . Probabilistic Engineering Mechanics, 10, 23-34, 1995.
4. Grigoriu, M., " Linear and non-linear systems with non-Gaussian white noise input" . Probabilistic Engineering Mechanics, 10, 171-179, 1995.
5. Grigoriu, M., " Applied non-Gaussian processes, example, theory simulation linear random vibration and MATLAB solutions" . Prentice Hall, New Jersey, 1995.
6. Pesechis, F.E., " Statistical dynamics of stable processes" , Physical review A, Vol.36, n.2, 15, 1987.
7. Jespersen, S., Metzler, S., Fogedby, H.C., " Lèvy flights in external force fields: langevin and fractional Fokker-Planck equations and their solutions, Physical review E, Vol.59, n.3, 1999.
8. Eliazar, I., Klafter, J., " Lèvy-driven Langevin systems: targeted stochasticity" , Journal of Statistical Physics, Vol.111, n. 3/4, 2003.
9. Chechkin, A., Gonchar, V., Klafter, J., Metzler, R., Tanatorov, L., " Stationary states of non linear oscillators driven by Lèvy noise" , Chemical Physics 284, pp. 233-251, 2002.
10. Gonchar, V., Tanatorov, L.V., Chechkin, A., " Stationary solutions of the fractional kinetic equation with symmetric power-law potential" , Theoretical and mathematical Physics, 131(1), 582-594, 2002.
11. Chambers, J.M., Mellows, C.L., Stuck, B.W., " A method for simulating stable random variables" , Journal of the American Statistical Association, Vol.71, n.154, 1976.
12. Janicki, A., Weron, A., " Computer simulation of attractors in stochastic models with α-stable noise" , Mathematics and Computers in Simulation, 39, pp.9-19, 1995.
13. Janicki, A., Weron, A., " Can one see α-stable variable and processes?" , Statistical Science, Vol.9, n.1, pp.109-126, 1994.
14. Di Paola, M., Falsone, G., " Itô and Statonovich integral for delta correlated processes" . Probabilistic Engineering Mechanics, 8, 197-208, 1993.
15. Di Paola, M., Pirrotta, A., " Non-linear systems under impulsive parametric input" . International Journal of Non-linear Mechanics, 34, 843-851, 1999.
16. Caddemi, S., Di Paola, M., " Non-linear system response for impulsive parametric input" . Journal of Applied Mechanics, 64, 642-647, 1997.
17. Wojtkiewicz, S.F., Johnson, E.A., Bergman, L.A., Grigoriu, M., Spencer, B.F., " Response of stochastic dynamical systems driver by additive Gaussian and Poisson white noise: solution of a forward Kolmogorov equation by a spectral finite difference method" , 168, 73-89, 1999.
18. Roberts, J.B., " System response to random impulses" , Journal of Sound and Vibration, 24, pp.23-34, 1972.
19. Gihman, J.I., Skorohod, A.V., " Stochastic differential equations" , Springer Verlag, Berlin 1972.
20. Iwankiewicz, R., Nielsen, S.R.K., " Dynamic response of non linear systems to Poisson distributed random impulses, Journal of Sound and Vibration, 156 (3), pp.407-423, 1992.
21. Di Paola, M., Failla, G., Stochastic response of linear and non linear systems to Alpha-Stable processes, submitted on Probabilistic Engineering Mechanics