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Abstrakty
An asymptotic behavior of a continuous time random walk is investigated in the case when the sequence of pairs of jump vectors and times between jumps is chain dependent.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
239--261
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Institute of Mathematics, University of Wrocław, 50-384 Wrocław, Poland
autor
- Institute of Mathematics, University of Wrocław, 50-384 Wrocław, Poland
Bibliografia
- [1] P. Becker-Kern, M. M. Meerschaert and H. P. Scheffler, Limit theorems for coupled continuous time random walks, Ann. Probab. 32 (2004), pp. 730-756.
- [2] P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968.
- [3] R. Durrett and S. I. Resnik, Functional limit theorems for dependent variables, Ann. Probab. 6 (1978), pp. 829-846.
- [4] A. Jurlewicz, Limit theorems for randomly coarse grained continuous-time random walks, Dissertationes Math. 431 (2005), pp. 1-45.
- [5] A. Jurlewicz, P. Becker-Kern, M. M. Meerschaert and H. P. Scheffler, Oracle continuous time random walk (2010), preprint available at the website http://www.stt.msu.edu/mcubed/OCTRW.pdf
- [6] A. Jurlewicz, A. Wyłomańska and P. Żebrowski, Coupled continuous-time random walk approach to the Rachev-Ruschendorf model for financial data, Phys. A 388 (2009), pp. 407-418.
- [7] M. M. Meerschaert, E. Nane and Y. Xiao, Correlated continuous time random walks, Statist. Probab. Lett. 79 (2009), pp. 1194-1202.
- [8] M. M. Meerschaert and E. Scalas, Coupled continuous time random walks in finance, Phys. A 370 (2006), pp. 114-118.
- [9] M. M. Meerschaert and H. P. Scheffler, Limit theorems for continuous-time random walks with infinite mean waiting times, J. Appl. Probab. 41 (2004), pp. 623-638.
- [10] M. M. Meerschaert and H. P. Scheffler, Triangular array limits for continuous-time random walks, Stochastic Process. Appl. 118 (2008), pp. 1606-1633.
- [11] G. L. O’Brien, Limit theorem for sums of chain-dependent processes, J. Appl. Probab. 11 (1974), pp. 582-587.
- [12] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge 1999.
- [13] W. Szczotka and P. Żebrowski, On fully coupled continuous time random walks, submitted to Appl. Math. (Warsaw).
- [14] V. Tejedor and R. Metzler, Anomalous diffusion in correlated continuous time random walks, J. Phys. A: Math. Theor. 43 (2010), 082002.
- [15] W. Whitt, Some useful functions for functional limit theorems, Math. Oper. Res. 5 (1980), pp. 67-85.
- [16] W. Whitt, Stochastic-Process Limits. An Introduction to Stochastic-Process Limits and Their Application to Queues, Springer, 2002.
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Bibliografia
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