Characteristic function for the stationary state of a one-dimensional dynamical system with Lévy noise

Theoretical and Mathematical Physics

Volumn 150, Issue 3, 2007, Pages 332-346

  Samorodnitsky, G ^a   Grigoriu, M ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

Characteristic function; Diffusion with jumps; It formula; L vy white noise; Stationary solution

Indexed keywords

EID: 33947396400     PISSN: 00405779     EISSN: 15739333     Source Type: Journal    
DOI: 10.1007/s11232-007-0025-0     Document Type: Article

References (13)

1. M. Grigoriu, Stochastic Calculus: Applications in Science and Engineering, Birkhäuser, Boston (2002).
2. M. Grigoriu, Probab. Eng. Mech., 19, 449-461 (2004).
3. A. V. Chechkin and V. Yu. Gonchar, JETP, 91, 635-651 (2000).
4. V. Yu. Gonchar, L. V. Tanatarov, and A. V. Chechkin, Theor. Math. Pbys., 131, 582-594 (2002).
5. G. Samorodnitsky and M. Grigoriu, Stochastic Process. Appl., 105, No. 3, 69-97 (2003).
6. T. G. Kurtz and P. Protter, Ann. Probab., 19, 1035-1070 (1991).
7. M. Grigoriu, Applied Non-Gaussian Processes: Examples, Theory, Simulation, Linear Random Vibration, and MATLAB Solutions, Prentice-Hall, Englewoods Cliffs, N. J. (1995).
8. B. V. Gnedenko, Course of Probability Theory [in Russian], Nauka, Moscow (1969)
9. English transl.: Theory of Probability (6th ed.), Gordon and Breach, Newark, N. J. (1997).
10. G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman and Hall, New York (1994).
11. P. Protter, Stochastic Integration and Differential Equations (Appl. Math. N. Y., Vol. 21), Springer, Berlin (1990).
12. S. Asmussen and J. Rosiński, J. Appl. Probab., 38, 482-493 (2001).
13. N. Fournier and S. Méléard, Bernoulli, 8, 537-558 (2002).