Large and small deviations of a string driven by a two-parameter Gaussian noise white in time

Journal of Applied Probability

Volumn 40, Issue 4, 2003, Pages 946-960

  Caithamer, Peter ^a,b  

^a UNITED STATES MILITARY ACADEMY   (United States)

^b NONE   (United States)

Author keywords

Large deviation; Small deviation; Stochastic wave equation; White noise

Indexed keywords

EID: 0442323010     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1067436092     Document Type: Article

References (17)

1. BELINSKIY, B. P. AND CAITHAMER, P. (2001). Energy of a string driven by a two-parameter Gaussian noise white in time. J. Appl. Prob. 38, 960-974.
2. BISWAS, S. K. AND AHMED, N. U. (1985). Stabilisation of systems governed by the wave equation in the presence of white noise. IEEE Trans. Automatic Control 30, 1043-1045.
3. CABAÑA, E. (1970). The vibrating string forced by white noise. Z. Wahrscheinlichkeitsth. 15, 111-130.
4. CABAÑA, E. (1972). On barrier problems for the vibrating string. Z. Wahrscheinlichkeitsth. 22, 13-24.
5. CONWAY, J. B. (1990). A Course in Functional Analysis. Springer, New York.
6. DALANG, R. C. AND FRANGOS, N. E. (1998). The stochastic wave equation in two spatial dimensions. Ann. Prob. 26, 187-212.
7. DUDLEY, R. (1967). The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1, 290-330.
8. DURRETT, R. (1995). Probability: Theory and Examples, 2nd edn. Duxbury, Belmont, CA.
9. ELSHAMY, M. (1995). Randomly perturbed vibrations. J. Appl. Prob. 32, 417-428.
10. ELSHAMY, M. (1996). Stochastic models of damped vibrations. J. Appl. Prob. 33, 1159-1168.
11. FERNIQUE, X. (1975). Régularité des trajectoires des fonctions aléatoires gaussiennes. In École d'Été de Probabilités de Saint-Flour IV (Lecture Notes Math. 480), ed. P.-L. Hennequin, Springer, Berlin, pp. 1-96.
12. LEDOUX, M. (1996). Isoperimetry and Gaussian analysis. In Lectures on Probability Theory and Statistics (Lecture Notes Math. 1648), Springer, Berlin, pp. 165-294.
13. LI, W. AND SHAO, Q. (2001). Gaussian processes: inequalities, small ball probabilities and applications. In Handbook of Statistics, Vol. 19, Stochastic Processes: Theory and Methods, eds C. R. Rao and D. Shanbhag, North-Holland, Amsterdam, pp. 533-597.
14. MILLER, R. N. (1990). Tropical data assimilation with simulated data: the impact of the tropical ocean and global atmosphere thermal array for the ocean. J. Geophys. Res. Oceans 95, 11461-11482.
15. ORSINGHER, E. (1982). Randomly forced vibrations of a string. Ann. Inst. H. Poincaré B 18, 367-394.
16. ORSINGHER, E. (1984). Damped vibrations excited by white noise. Adv. Appl. Prob. 16, 562-584.
17. ORSINGHER, E. (1989). On the maximum of Gaussian Fourier series emerging in the analysis of random vibrations. J. Appl. Prob. 26, 182-188.