Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 4, Pages 684–703 (Mi tvp2460)  

This article is cited in 32 scientific papers (total in 32 papers)

Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics

V. N. Kolokoltsov

Nottingham Trent University

Abstract: Functional limit theorems for continuous-time random walks (CTRW) are found in the general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional dynamics. Probabilistic interpretation of generalized fractional evolution is given in terms of the random time change (subordination) by means of hitting times processes.

Keywords: fractional stable distributions, anomalous diffusion, fractional derivatives, limit theorems, continuous-time random walks, time change, Lйvy subordinators, hitting time processes.

DOI: https://doi.org/10.4213/tvp2460

Full text: PDF file (2223 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2009, 53:4, 594–609

Bibliographic databases:

Received: 30.11.2007

Citation: V. N. Kolokoltsov, “Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics”, Teor. Veroyatnost. i Primenen., 53:4 (2008), 684–703; Theory Probab. Appl., 53:4 (2009), 594–609

Citation in format AMSBIB
\Bibitem{Kol08}
\by V.~N.~Kolokoltsov
\paper Generalized Continuous-Time Random Walks, Subordination by Hitting Times, and Fractional Dynamics
\jour Teor. Veroyatnost. i Primenen.
\yr 2008
\vol 53
\issue 4
\pages 684--703
\mathnet{http://mi.mathnet.ru/tvp2460}
\crossref{https://doi.org/10.4213/tvp2460}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2766141}
\zmath{https://zbmath.org/?q=an:05701636}
\transl
\jour Theory Probab. Appl.
\yr 2009
\vol 53
\issue 4
\pages 594--609
\crossref{https://doi.org/10.1137/S0040585X97983857}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000273141700002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-73549104035}


Linking options:
  • http://mi.mathnet.ru/eng/tvp2460
  • https://doi.org/10.4213/tvp2460
  • http://mi.mathnet.ru/eng/tvp/v53/i4/p684

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Orsingher E., Polito F., Sakhno L., “Fractional non-linear, linear and sublinear death processes”, J. Stat. Phys., 141:1 (2010), 68–93  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Hahn M.G., Kobayashi K., Umarov S., “Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion”, Proc. Amer. Math. Soc., 139:2 (2011), 691–705  crossref  mathscinet  zmath  isi  elib  scopus
    3. Hahn M., Umarov S., “Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations”, Fract. Calc. Appl. Anal., 14:1 (2011), 56–79  crossref  mathscinet  zmath  isi  elib  scopus
    4. Jara M., Komorowski T., “Limit theorems for some continuous-time random walks”, Adv. in Appl. Probab., 43:3 (2011), 782–813  crossref  mathscinet  zmath  isi  scopus
    5. Meerschaert M.M., Straka P., Zhou Yu., McGough R.J., “Stochastic solution to a time-fractional attenuated wave equation”, Nonlinear Dynam., 70:2 (2012), 1273–1281  crossref  mathscinet  isi  elib  scopus
    6. Bolster D., Meerschaert M.M., Sikorskii A., “Product rule for vector fractional derivatives”, Fract. Calc. Appl. Anal., 15:3 (2012), 463–478  crossref  mathscinet  zmath  isi  elib  scopus
    7. Kochubei A.N., “Fractional-parabolic systems”, Potential Anal., 37:1 (2012), 1–30  crossref  mathscinet  zmath  isi  elib  scopus
    8. Fedotov S., Falconer S., “Subdiffusive master equation with space-dependent anomalous exponent and structural instability”, Phys. Rev. E, 85:3 (2012), 031132, 6 pp.  crossref  mathscinet  adsnasa  isi  elib  scopus
    9. Straka P., Meerschaert M.M., McGough R.J., Zhou Yu., “Fractional wave equations with attenuation”, Fract. Calc. Appl. Anal., 16:1 (2013), 262–272  crossref  mathscinet  zmath  isi  elib  scopus
    10. Meerschaert M.M., Straka P., “Inverse Stable Subordinators”, Math. Model. Nat. Phenom., 8:2 (2013), 1–16  crossref  mathscinet  zmath  isi  elib  scopus
    11. N. S. Arkashov, V. A. Seleznev, “On one model of sub- and superdiffusion on topological spaces with a self-similar structure”, Theory Probab. Appl., 60:2 (2016), 173–186  mathnet  crossref  crossref  isi  elib
    12. Kolokoltsov V., “on Fully Mixed and Multidimensional Extensions of the Caputo and Riemann-Liouville Derivatives, Related Markov Processes and Fractional Differential Equations”, Fract. Calc. Appl. Anal., 18:4 (2015), 1039–1073  crossref  mathscinet  zmath  isi  elib  scopus
    13. Lv L., Xiao J., Fan L., Ren F., “Correlated Continuous Time Random Walk and Option Pricing”, Physica A, 447 (2016), 100–107  crossref  mathscinet  adsnasa  isi  scopus
    14. Hernandez-Hernandez M.E., Kolokoltsov V.N., “On the solution of two-sided fractional ordinary differential equations of Caputo type”, Fract. Calc. Appl. Anal., 19:6 (2016), 1393–1413  crossref  mathscinet  zmath  isi  scopus
    15. Kelbert M., Konakov V., Menozzi S., “Weak error for Continuous Time Markov Chains related to fractional in time P(I)DEs”, Stoch. Process. Their Appl., 126:4 (2016), 1145–1183  crossref  mathscinet  zmath  isi  elib  scopus
    16. Baeumer B., Straka P., “Fokker–Planck and Kolmogorov backward equations for continuous time random walk scaling limits”, Proc. Amer. Math. Soc., 145:1 (2017), 399–412  crossref  mathscinet  zmath  isi  elib  scopus
    17. Hernandez-Hernandez M.E., Kolokoltsov V.N., Toniazzi L., “Generalised Fractional Evolution Equations of Caputo Type”, Chaos Solitons Fractals, 102 (2017), 184–196  crossref  mathscinet  zmath  isi  scopus
    18. Leonenko N.N., Papic I., Sikorskii A., Suvak N., “Correlated Continuous Time Random Walks and Fractional Pearson Diffusions”, Bernoulli, 24:4B (2018), 3603–3627  crossref  mathscinet  zmath  isi  scopus
    19. Orsingher E., Ricciuti C., Toaldo B., “On Semi-Markov Processes and Their Kolmogorov'S Integro-Differential Equations”, J. Funct. Anal., 275:4 (2018), 830–868  crossref  mathscinet  zmath  isi  scopus
    20. Leonenko N.N., Papic I., Sikorskii A., Suvak N., “Ehrenfest-Brillouin-Type Correlated Continuous Time Random Walk and Fractional Jacobi Diffusion”, Theory Probab. Math. Stat., 99 (2018), 123–133  mathscinet  isi
    21. Meerschaert M.M., Toaldo B., “Relaxation Patterns and Semi-Markov Dynamics”, Stoch. Process. Their Appl., 129:8 (2019), 2850–2879  crossref  isi
    22. V. N. Kolokoltsov, “Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions”, Math. Notes, 106:5 (2019), 740–756  mathnet  crossref  crossref  mathscinet  isi  elib
    23. Kochubei A.N., Kondratiev Yu., da Silva J.L., “From Random Times to Fractional Kinetics”, Interdiscip. Stud. Complex Syst., 2019, no. 16, 5–32  crossref  isi
    24. Kolokoltsov V.N., “The Probabilistic Point of View on the Generalized Fractional Partial Differential Equations”, Fract. Calc. Appl. Anal., 22:3 (2019), 543–600  crossref  mathscinet  isi
    25. Duan R., Li J., Chen J., “Mode-Dependent Non-Fragile Observer-Based Controller Design For Fractional-Order T-S Fuzzy Systems With Markovian Jump Via Non-Pdc Scheme”, Nonlinear Anal.-Hybrid Syst., 34 (2019), 74–91  crossref  mathscinet  isi
    26. Capitanelli R., D'Ovidio M., “Fractional Equations Via Convergence of Forms”, Fract. Calc. Appl. Anal., 22:4 (2019), 844–870  crossref  mathscinet  isi
    27. Beghin L., Macci C., Ricciuti C., “Random Time-Change With Inverses of Multivariate Subordinators: Governing Equations and Fractional Dynamics”, Stoch. Process. Their Appl., 130:10 (2020), 6364–6387  crossref  mathscinet  isi
    28. Capitanelli R., D'Ovidio M., “Delayed and Rushed Motions Through Time Change”, ALEA-Latin Am. J. Probab. Math. Stat., 17:1 (2020), 183–204  crossref  mathscinet  isi
    29. Savov M., Toaldo B., “Semi-Markov Processes, Integro-Differential Equations and Anomalous Diffusion-Aggregation”, Ann. Inst. Henri Poincare-Probab. Stat., 56:4 (2020), 2640–2671  crossref  mathscinet  isi
    30. Leonenko N.N., Papic I., Sikorskii A., Suvak N., “Approximation of Heavy-Tailed Fractional Pearson Diffusions in Skorokhod Topology”, J. Math. Anal. Appl., 486:2 (2020), 123934  crossref  mathscinet  isi
    31. Ascione G., Pirozzi E., Toaldo B., “On the Exit Time From Open Sets of Some Semi-Markov Processes”, Ann. Appl. Probab., 30:3 (2020), 1130–1163  crossref  mathscinet  isi
    32. Pachon A., Polito F., Ricciuti C., “On Discrete-Time Semi-Markov Processes”, Discrete Contin. Dyn. Syst.-Ser. B, 26:3 (2021), 1499–1529  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:501
    Full text:146
    References:71

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021