Continuous-time random walk approach to modeling of relaxation: The role of compound counting processes

Acta Physica Polonica B

Volumn 39, Issue 5, 2008, Pages 1055-1066

  Jurlewicz, Agnieszka ^a   Weron, Karina ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS TIME SYSTEMS; PHYSICS; SEMICONDUCTOR DOPING;

CONTINUOUS TIMES; COUNTING PROCESSES; NEW CLASSES; RANDOM NUMBERS; RANDOM WALKS; RELAXATION MODELS; SPATIO TEMPORALS;

RANDOM PROCESSES;

EID: 55249086283     PISSN: 05874254     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (33)

1. R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000).
2. E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965).
3. H. Scher, E.W. Montroll, Phys. Rev. B12, 2455 (1975).
4. R. Metzler, E. Barkai, J. Klafter, Europhys. Lett. 46, 431 (1999).
5. E. Barkai, R. Metzler, J. Klafter, Phys. Rev. E61, 132 (2000).
6. I.M. Sokolov, Phys. Rev. E63, 011104 (2000);
7. Phys. Rev. E66, 041101 (2002).
8. A.A. Stanislavsky, Theor. Math. Phys. 138, 418 (2004).
9. E. Gudowska-Nowak, K. Weron, Phys. Rev. E65, 011103 (2001).
10. A. Jurlewicz, Appl. Math. 30, 325 (2003).
11. A. Jurlewicz, Diss. Math. 431, 1 (2005).
12. K. Weron, A. Jurlewicz, M. Magdziarz, Acta Phys. Pol. B 36, 1855 (2005).
13. E. Gudowska-Nowak, K. Bochenek, A. Jurlewicz, K. Weron, Phys. Rev. E72, 061101 (2005).
14. M. Magdziarz, K. Weron, Acta Phys. Pol. B 37, 1617 (2006).
15. M. Magdziarz, K. Weron, Physica A 367, 1 (2006).
16. M. Magdziarz, A. Weron, K. Weron, Phys. Rev. E75, 016708 (2007).
17. M. Magdziarz, A. Weron, Phys. Rev. E75, 056702 (2007).
18. M. Magdziarz, A. Weron, Phys. Rev. E76, 066708 (2007).
19. K. Burnecki, J. Janczura, M. Magdziarz, A. Weron, Acta Phys. Pol. B 39, 1041 (2008), these proceedings.
20. K. Weron, M. Kotulski, Physica A 232, 180 (1996).
21. M.M. Meerschaert, H.-P. Scheffler, J. Appl. Probab. 41, 623 (2004).
22. A. Piryatinska, A.I. Saichev, W.A. Woyczynski, Physica A 349, 375 (2005).
23. W. Feller, An Introduction to Probability Theory and Its Applications, vol. 2, Wiley, New York 1966.
24. A.K. Jonscher, Universal Relaxation Law, Chelsea Dielectrics Press, London 1996.
25. M. Kotulski, J. Stat. Phys. 81, 777 (1995).
26. V.M. Zolotarev, One-Dimensional Stable Distributions, American Mathematical Society, Providence 1986.
27. A. Janicki, A. Weron, Simulation and Chaotic Behavior of α-Stable Stochastic Processes, Marcel Dekker, New York 1994.
28. G. Samorodnitsky, M.S. Taqqu, Stable Non-Gaussian Random Processes. Stochastic Models with Infinite Variance, Chapman and Hall, New York, London 1994.
29. R.L. Dobrushin, Usp. Mat. Nauk. 10(64), 157 (1955) (in Russian).
30. A. Gut, Stopped Random Walks. Limit Theorems and Applications, Springer, New York 1988.
31. V.N. Kolokoltsov, V.Yu. Korolev, V.V. Uchaikin, J. Math. Sci. 105, 2569 (2001).
32. V.V. Uchaikin, J. Exper. Theor. Phys. 97, 810 (2003).
33. V.E. Bening, V.Yu. Korolev, S. Koksharov, V.N. Kolokoltsov, J. Math. Sci. 146, 5950 (2007).