PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2010 | 8 | 5 | 699-708
Tytuł artykułu

Lévy flights and Lévy-Schrödinger semigroups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We analyze two different confining mechanisms for Lévy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Lévy-Schrödinger semigroups which induce so-called topological Lévy processes (Lévy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological Lévy process with the same invariant pdf and in reverse.
Wydawca

Czasopismo
Rocznik
Tom
8
Numer
5
Strony
699-708
Opis fizyczny
Daty
wydano
2010-10-01
online
2010-07-22
Twórcy
  • Institute of Physics, University of Opole, 45-052, Opole, Poland, pgar@uni.opole.pl
Bibliografia
  • [1] M. F. Shlesinger, G. M. Zaslavsky, U. Frisch (Eds.), Lévy Flights and Related Topics in Physics, Lecture Notes in Physics (Springer-Verlag, Berlin, 1995)
  • [2] P. Garbaczewski, M. Wolf, A. Weron (Eds.), Chaos: The interplay between deterministic and stochastic behavior, Lecture Notes in Physics (Springer-Verlag, Berlin, 1995)
  • [3] D. Applebaum, Lévy processes and stochastic calculus (Cambridge University Press, 2004)
  • [4] K.-I. Sato, Lévy processes and infinitely divisible distributions (Cambridge University Press, 1999)
  • [5] P. Garbaczewski, J. R. Klauder, R. Olkiewicz, Phys. Rev. E 51, 4114 (1995) http://dx.doi.org/10.1103/PhysRevE.51.4114[Crossref]
  • [6] P. Garbaczewski, R. Olkiewicz, J. Math. Phys. 40, 1057 (1999) http://dx.doi.org/10.1063/1.532706[Crossref]
  • [7] P. Garbaczewski and R. Olkiewicz, J. Math. Phys. 41, 6843 (2000) http://dx.doi.org/10.1063/1.1290054[Crossref]
  • [8] S. Jespersen, R. Metzler, H. C. Fogedby, Phys. Rev. E 59, 2736 (1999) http://dx.doi.org/10.1103/PhysRevE.59.2736[Crossref]
  • [9] P. D. Ditlevsen, Phys. Rev. E 60, 172 (1999) http://dx.doi.org/10.1103/PhysRevE.60.172[Crossref]
  • [10] V. V. Janovsky et al., Physica A 282, 13 (2000) http://dx.doi.org/10.1016/S0378-4371(99)00565-8[Crossref]
  • [11] A. Chechkin et al., Chem. Phys. 284, 233 (2002) http://dx.doi.org/10.1016/S0301-0104(02)00551-7[Crossref]
  • [12] A. A. Dubkov, B. Spagnolo, Acta Phys. Pol. A 38, 1745 (2007)
  • [13] A. A. Dubkov, B. Spagnolo, V. V. Uchaikin, Int. J. Bifurcat. Chaos 18, 2549 (2008)
  • [14] V. V. Belik, D. Brockmann, New. J. Phys. 9, 54 (2007) http://dx.doi.org/10.1088/1367-2630/9/3/054[Crossref]
  • [15] N. Cufaro Petroni, M. Pusterla, Physica A 388, 824 (2009) http://dx.doi.org/10.1016/j.physa.2008.11.035[Crossref]
  • [16] D. Brockmann, I. Sokolov, Chem. Phys. 284, 409 (2002) http://dx.doi.org/10.1016/S0301-0104(02)00671-7[Crossref]
  • [17] D. Brockmann, T. Geisel, Phys. Rev. Lett. 90, 170601 (2003) http://dx.doi.org/10.1103/PhysRevLett.90.170601[Crossref]
  • [18] D. Brockmann, T. Geisel, Phys. Rev. Lett. 91, 048303 (2003) http://dx.doi.org/10.1103/PhysRevLett.91.048303[Crossref]
  • [19] M. C. Mackey, M. Tyran-Kamińska, J. Stat. Phys. 124, 1443 (2006) http://dx.doi.org/10.1007/s10955-006-9181-0[Crossref]
  • [20] J. C. Zambrini, Phys. Rev. A 35, 3631 (1987) http://dx.doi.org/10.1103/PhysRevA.35.3631[Crossref]
  • [21] P. Garbaczewski, Acta Phys. Pol. B 40, 1353 (2009)
  • [22] P. Garbaczewski, Phys. Rev. E 78, 031101 (2008) http://dx.doi.org/10.1103/PhysRevE.78.031101[Crossref]
  • [23] H. Risken, The Fokker-Planck equation (SpringerVerlag, Berlin, 1989)
  • [24] I. S. Gradshteyn, I. M. Ryzhik, Table of integrals, series and products (Academic Press, NY, 2007)
  • [25] J. N. Kapur, H. K. Kesavan, Entropy Optimization Principles with Applications (Academic Press, Boston, 1992)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-009-0156-z
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.