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Chain dependent continuous time random walk

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
239--261
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Institute of Mathematics, University of Wrocław, 50-384 Wrocław, Poland
  • 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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b6941acf-111d-4e91-9763-df93faf6a415
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