On a stochastic wave equation driven by a non-Gaussian Lévy process

Journal of Theoretical Probability

Volumn 23, Issue 1, 2010, Pages 328-343

  Bo, Lijun ^a,b   Shi, Kehua ^b   Wang, Yongjin ^b  

^a XIDIAN UNIVERSITY   (China)

^b NANKAI UNIVERSITY   (China)

Author keywords

Damped wave equation; Invariant measure; L vy noise

Indexed keywords

EID: 75749128215     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-009-0228-4     Document Type: Article

References (15)

1. Barbu, V., Da Prato, G., Tubaro, L.: Stochastic wave equations with dissipative damping. Stoch. Process. Appl. 117, 1001-1013 (2007).
2. Bo, L., Shi, K., Wang, Y.: Stochastic wave equation driven by compensated Poisson random measure. Preprint (2008).
3. d. J. Differ. Equ. 244, 170-187 (2008).
4. Brzeniak, Z., Maslowski, B., Seidler, J.: Stochastic nonlinear beam equations. Probab. Theory Relat. Fields 132, 119-149 (2005).
5. Chow, P.: Stochastic wave equation with polynomial nonlinearity. Ann. Appl. Probab. 12, 361-381 (2002).
6. Chow, P.: Asymptotics of solutions to semilinear stochastic wave equations. Ann. Appl. Probab. 16, 757-789 (2006).
7. Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam (1981).
8. Lions, J. L.: Equations différentielles operationelles et problèmes aux limits. Springer, Berlin (1961).
9. Peszat, S., Zabczyk, J.: Stochastic heat and wave equations driven by an impulsive noise. In: Da Prato, G., Tubaro, L. (eds.) Stochastic Partial Differential Equations and Applications, VII. Lect. Notes Pure Appl., vol. 245, pp. 229-242. Chapman & Hall/CRC, Boca Raton (2006).
10. Peszat, S., Zabczyk, J.: Stochastic Partial Differential Equations with Lévy noise: An Evolution Equation Approach. Encyclopedia of Mathematics and Its Applications, vol. 113. Cambridge University Press, Cambridge (2007).
11. Sato, K.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999).
12. Schiff, L.: Nonlinear meson theory of nuclear forces, I. Phys. Rev. 84, 1-9 (1951).
13. Segal, I.: The global Cauchy problem for a relativistic scalar field with power interaction. Bull. Soc. Math. Fr. 91, 129-135 (1963).
14. Temam, R.: Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 2nd edn. Springer, New York (1997).
15. Zeidler, E.: Nonlinear Functional Analysis and Its Applications, II/B, Nonlinear Monotone Operators. Springer, New York (1990).