On the solutions of linear odd-order heat-type equations with random initial conditions

Journal of Statistical Physics

Volumn 127, Issue 4, 2007, Pages 721-739

  Beghin, L ^a   Kozachenko, Yu ^b   Orsingher, E ^a   Sakhno, L ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV   (Ukraine)

Author keywords

Harmonizable processes; Higher order heat type equations; subGaussian processes

Indexed keywords

EID: 34247508577     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-007-9309-x     Document Type: Article

References (34)

1. L. Beghin, K. Hochberg and E. Orsingher, Stoch. Process. Appl. 85:209-223 (2000).
2. L. Beghin, V. P. Knopova, N. N. Leonenko and E. Orsingher, J. Stat. Phys. 99(3/4):769-781 (2000).
3. L. Beghin and E. Orsingher, Stoch. Process. Appl. 115:1017-1040 (2005).
4. L. Beghin, E. Orsingher and T. Ragozina, Stoch. Process. Appl. 94:71-93 (2001).
5. V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes. Translations of Mathematical Monographs. 188 (AMS, American Mathematical Society, Providence, RI, 2000), 257 p.
6. J. L. Doob, Trans. Am. Math. Soc. 42:107-140 (1937).
7. C. W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1985).
8. R. Giuliano Antonini, Yu. V. Kozachenko and T. Nikitina, Rendiconti Accademia Nazionale delle Scienze XL. Memorie di Matematica e Applicazioni 121. XXVII:95-124 (2003).
9. K. J. Hochberg and E. Orsingher, Stoch. Proc. Appl. 52:273-292 (1994).
10. G. A. Hunt, Trans. Am. Math. Soc. 71:38-69 (1951).
11. J. K. Hunter and J. Scheurle, Physica D 32:253-268 (1988).
12. T. Iizuka, Phys. Lett. A 181:39-42 (1993).
13. T. Kakutani and H. Ono, J. Phys. Soc. Jpn. 26:1305-1318 (1969).
14. T. Kawahara, J. Phys. Soc. Jpn. 33:260-264 (1972).
15. V. P. Knopova, Random Oper. Stoch. Equ. 12(1):35-42 (2004).
16. Yu. V. Kozachenko, Dokl. Akad. Nauk Ukr. SSR, Ser. A. 9:14-16 (1984).
17. Yu. V. Kozachenko, Theory Probab. Math. Stat. 40:43-50 (1990).
18. Yu. V. Kozachenko and E. I. Ostrovskij, Theory Probab. Math. Stat. 32:45-56 (1986).
19. Yu. V. Kozachenko and I. Rozora, Random Oper. Stoch. Equ. 3:275-296 (2003).
20. Yu. V. Kozachenko and G. I. Slivka, Theor. Probab. Math. Statist. 69:67-83 (2004).
21. A. Lachal, Electron. J. Prob. 8(20):1-53 (2003).
22. N, preprint (2006).
23. M. J. Lighthill, Waves in Fluids (Cambridge University Press, Cambridge, 1978).
24. M. Loève, Probability Theory. Foundations. Random sequences (D. van. Nostrand Co., Inc. XV., New York, 1955) 515 p.
25. T. Mikosch and R. Norvaiša, Bernoulli 6(3):401-434 (2000).
26. H. Nagashima, Phys. Lett. A 105:439-442 (1984).
27. H. Nagashima and M. Kuwahara, J. Phys. Soc. Jpn. 105:439-442 (1981).
28. R. Norvaiša and G. Samorodnitsky, Ann. Probab. 22(4): 1904-1929 (1994).
29. E. Orsingher, Lith. Math. J. 31:321-334 (1991).
30. B. S. Rajput and J. Rosinski, Probab. Theory Rel. Fields 82:451-487 (1989).
31. F. Tappert, Nonlinear Wave Motion, Lecture Notes in Applied Math. (AMS) vol. 15, pp. 215-216 (1974).
32. M. Wadati, J. Phys. Soc. Jpn. 52:2642-2648 (1983).
33. G. B. Whitham, Linear nad Nonlinear Waves (John Wiley & Sons Inc., New York). Reprint of the 1974 original, A Wiley-Interscience Publ. (1999).
34. K. Yoshimura and S. Watanabe, J. Phys. Soc. Jpn. 51:3028-3055 (1982).