An alternative expression for stochastic dynamical systems with parametric Poisson white noise

Probabilistic Engineering Mechanics

Volumn 32, Issue , 2013, Pages 1-4

  Sun, Xu ^a   Duan, Jinqiao ^b,c   Li, Xiaofan ^c  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Illinois Institute of Technology   (United States)

Author keywords

Non Gaussian white noise; Nonlinear systems; Poisson white noise; Random vibration; Stochastic dynamics

Indexed keywords

CORRECTION TERMS; ITO INTEGRAL; NON-GAUSSIAN; NUMERICAL IMPLEMENTATION; RANDOM VIBRATIONS; STOCHASTIC DYNAMICAL SYSTEM; STOCHASTIC DYNAMICS;

GAUSSIAN NOISE (ELECTRONIC); NONLINEAR SYSTEMS;

WHITE NOISE;

EID: 84873845315     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.probengmech.2012.12.006     Document Type: Article

References (19)

1. D. Applebaum Levy processes and stochastic calculus 2nd ed 2009 Cambridge University Press
2. S. Caddemi, and M. Di Paola Ideal and physical white noise in stochastic analysis International Journal of Non-linear Mechanics 31 5 1996 581 590 (Pubitemid 126360113)
3. M. Di Paola, and G. Falsone Ito and Stratonovich integrals for delta-correlated processes Probabilistic Engineering Mechanics 8 1993 197 208
4. M. Di Paola, and G. Falsone Stochastic dynamics of non-linear systems driven by non-normal delta-correlated processes ASME Journal of Applied Mechanics 60 1993 141 148
5. M. Di Paola, and A. Pirrotta Non-linear systems under impulsive parametric input International Journal of Non-linear Mechanics 34 1999 843 851 (Pubitemid 129537044)
6. M. Grigoriu The Ito and Stratonovich integrals for stochastic differential equations with Poisson white noise Probabilistic Engineering Mechanics 13 1998 175 182 (Pubitemid 128393890)
7. S.L.J. Hu Closure on discussion by Di Paola, M. and Falsone, G., on response of dynamic systems excited by non-Gaussian pulse processes ASCE Journal of Engineering Mechanics 120 1994 2472 2474
8. R.A. Ibrahim Parametric random vibration 1985 Research Studies Press
9. D. Kincaid, and W. Cheney Numerical analysis mathematics of scientific computing 2002 Brooks/Cole
10. T. Kurtz, E. Pardoux, and P. Protter Stratonovich stochastic differential equations driven by general martingales Annales de l Institut Henri Poincare-Probabilities et Statistiques 31 1995 351 377
11. S.I. Marcus Modeling and analysis of stochastic differential equations driven by point processes IEEE Transactions on Information Theory IT-24 1978 164 172
12. S.I. Marcus Modeling and approximation of stochastic differential driven by semimartingales Stochastics 4 1981 223 245
13. A. Pirrotta Non-linear systems under delta correlated processes handled by perturbation theory Probabilistic Engineering Mechanics 13 1998 283 290 (Pubitemid 128431645)
14. C. Proppe The Wong-Zakai theorem for dynamical systems with parametric Poisson white noise excitation International Journal of Engineering Science 40 2003 1165 1178 (Pubitemid 34440694)
15. C.W.S. To Nonlinear random vibration analytical techniques and applications 2000 Swets and Zeitlinger Publishers
16. E. Wong, and M. Zakai On the relation between ordinary and stochastic differential equations International Journal of Engineering Science 3 1965 213 229
17. Y. Yong, and Y.K. Lin Exact stationary response solution for second order nonlinear systems under parametric and external white noise excitations Journal of Applied Mechanics, Transactions of the American Society of Mechanical Engineers 54 1987 414 418
18. Y. Zheng, and W.Q. Zhu Stochastic averaging of quasi-linear systems driven by Poisson white noise Probabilistic Engineering Mechanics 25 2010 99 107
19. Zheng Y, Zhu WQ. Stochastic averaging of strongly nonlinear oscillators under Poisson white noise excitation. In: IUTAM symposium on nonlinear stochastic dynamics and control, 2010. p. 147-55.