Universal record statistics of random walks and lévy flights

Physical Review Letters

Volumn 101, Issue 5, 2008, Pages

  Majumdar, Satya N ^a   Ziff, Robert M ^b  

^a UNIVERSITÉ PARIS SUD   (France)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL ANALYSIS; STANDARDS; STATISTICAL METHODS; TIME SERIES ANALYSIS;

ASYMPTOTIC BEHAVIORS; RANDOM WALKERS; RANDOM WALKS; STANDARD DEVIATION; TIME-SERIES;

RANDOM PROCESSES;

EID: 49149086595     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.101.050601     Document Type: Article

References (37)

1. D.V. Hoyt, Climatic Change CLCHDX 3, 243 (1981);
2. R.E. Benestad, Climate Res. 25, 3 (2003). CLREEW 0936-577X 10.3354/cr025003
3. S. Redner and M.R. Petersen, Phys. Rev. E 74, 061114 (2006). PLEEE8 1063-651X 10.1103/PhysRevE.74.061114
4. N.C. Matalas, Climatic Change CLCHDX 37, 89 (1997);
5. R.M. Vogel, A. Zafirakou-Koulouris, and N.C. Matalas, Water Resour. Res. WRERAQ 0043-1397 37, 1723 (2001). 10.1029/2001WR900019
6. G. Barlevy, Rev. Economic Stud. 0034-6527 69, 65 (2002); 10.1111/1467-937X.00198
7. G. Barlevy and H.N. Nagaraja, J. Appl. Probab. JPRBAM 0021-9002 43, 1119 (2006). 10.1239/jap/1165505212
8. D. Gembris, J.G. Taylor, and D. Suter, Nature (London) 417, 506 (2002). NATUAS 0028-0836 10.1038/417506a
9. N. Glick, Am. Math. Mon. 85, 2 (1978). AMMYAE 0002-9890 10.2307/2978044
10. E. Ben-Naim, S. Redner, and F. Vazquez, Europhys. Lett. 77, 30005 (2007). EULEEJ 0295-5075 10.1209/0295-5075/77/30005
11. B. Alessandro, C. Beatrice, G. Bertotti, and A. Montorsi, J. Appl. Phys. 68, 2901 (1990). JAPIAU 0021-8979 10.1063/1.346423
12. K.N. Chandler, J. R. Stat. Soc. Ser. B. Methodol. JSTBAJ 0035-9246 14, 220 (1952).
13. V.B. Nevzorov, Theory Probab. Appl. 32, 201 (1987). TPRBAU 0040-585X 10.1137/1132032
14. B.C. Arnold, N. Balakrishnan, and H.N. Nagaraja, Records (Wiley, New York, 1998).
15. B. Schmittmann and R.K.P. Zia, Am. J. Phys. 67, 1269 (1999). AJPIAS 0002-9505 10.1119/1.19114
16. P. Sibani and P.B. Littlewood, Phys. Rev. Lett. 71, 1482 (1993); PRLTAO 0031-9007 10.1103/PhysRevLett.71.1482
17. P.E. Andersen, H.J. Jensen, L.P. Oliveira, and P. Sibani, Complexity 10, 49 (2004). COMPFS 1076-2787 10.1002/cplx.20049
18. H.A. Orr, Nat. Rev. Genet. 1471-0056 6, 119 (2005). 10.1038/nrg1523
19. J. Krug and C. Karl, Physica (Amsterdam) 318A, 137 (2003); PHYSAG 0031-8914
20. J. Krug and K. Jain, Physica (Amsterdam) 358A, 1 (2005); PHYSAG 0031-8914
21. K. Jain and J. Krug, J. Stat. Mech. 1742-5468 (2005) P04008. 10.1088/1742-5468/2005/04/P04008
22. E. Ben-Naim and P.L. Krapivsky, J. Stat. Mech. 1742-5468 (2005) L10002; 10.1088/1742-5468/2005/10/L10002
23. C. Sire, S.N. Majumdar, and D.S. Dean, J. Stat. Mech. 1742-5468 (2006) L07001; 10.1088/1742-5468/2006/07/L07001
24. I. Bena and S.N. Majumdar, Phys. Rev. E 75, 051103 (2007). PLEEE8 1063-651X 10.1103/PhysRevE.75.051103
25. J. Krug, J. Stat. Mech. 1742-5468 (2007) P07001. 10.1088/1742-5468/2007/ 07/P07001
26. W. Feller An Introduction to Probability Theory and Its Applications (Wiley, New York, 1968).
27. S. Asmussen, Applied Probability and Queues (Springer, New York, 2003);
28. M.J. Kearney, J. Phys. A JPHAC5 0305-4470 37, 8421 (2004). 10.1088/0305-4470/37/35/002
29. R.J. Williams, Introduction to the Mathematics of Finance (AMS, Providence, 2006);
30. M. Yor, Exponential Functionals of Brownain Motion and Related Topics (Springer, Berlin, 2000).
31. E. Sparre Andersen, Math. Scand. 1, 263 (1953); MTSCAN 0025-5521
32. E. Sparre Andersen Math. Scand. 2, 195 (1954); MTSCAN 0025-5521
33. see also.
34. J. Pitman and M. Yor, Ann. Probab. 25, 855 (1997). APBYAE 0091-1798 10.1214/aop/1024404422
35. S.R. Finch, Excursion Durations, http://algo.inria.fr/bsolve (2008).
36. S.R. Finch, Mathematical Constants (Cambridge University Press, Cambridge, U.K., 2003), pp. 284-292.
37. C. Godreche and J.M. Luck (unpublished).