Run length statistics and the hurst exponent in random and birth-death random walks

Chaos, Solitons and Fractals

Volumn 7, Issue 9, 1996, Pages 1333-1341

  Tapiero, Charles S ^a   Vallois, Pierre ^b  

^a ESSEC BUSINESS SCHOOL   (France)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001086947     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/0960-0779(96)00032-X     Document Type: Article

References (11)

1. H. E. Hurst, Long-term storage capacity of reservoirs. Trans. Am. Soc. Civil Engrs 770-808 (1951).
2. E. Peters Edgar, Chaos and Order in the Capital Markets. Wiley, New York (1991).
3. T. H. Otway, Records of the Florentine proveditori degli cambiatori: An example of an antipersistent time series in economics. Chaos, Solitons & Fractals 5, 103-107 (1995).
4. J. P. Imhoff, On the range of Brownian motion and its inverse process. Ann. Prob. 13(3), 1011-1017 (1985).
5. J. P. Imhoff, A construction of the Brownian motion path from BES (3) pieces. Stochastic Proc. Appl. 43, 345-353 (1992).
6. P. Vallois, Diffusion arrêtée au premier instant où le processus de l'amplitude atteint un niveau donné. Stochastics and Stochastic Reports 43, 93-115 (1993).
7. P. Vallois, On the range process of a Bernoulli random walk. Proceedings of the Sixth International Symposium on Applied Stochastic Models and Data Analysis, edited by J. Janssen and C. H. Skiada, Vol. II, pp. 1020-1031. World Scientific, Singapore (1995).
8. P. Vallois, The range of a simple random walk on ℤ. J. Appl. Probability (to appear).
9. P. Vallois and C. S. Tapiero, Moments of an amplitude process in a random walk: computation and application. Rech. Operationnelle/Opn Res. (RAIRO), 29, 1-17 (1995).
10. P. Vallois and C. S. Tapiero, The average run length for the control of the range in asymmetric random walks. Preprint, ESSEC, Cergy Pontoise (1995).
11. W. Feller, The asymptotic distribution of the range of sums of independent random variables. Ann. Math. Stat. 22, 427-432 (1951).