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Multi angle Time changes of stochastic processes: convergence and heat kernel estimates

Auteurs : Kumagai, Takashi (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In recent years, interest in time changes of stochastic processes according to irregular measures has arisen from various sources. Fundamental examples of such time-changed processes include the so-called Fontes-Isopi-Newman (FIN) diffusion and fractional kinetics (FK) processes, the introduction of which were partly motivated by the study of the localization and aging properties of physical spin systems, and the two- dimensional Liouville Brownian motion, which is the diffusion naturally associated with planar Liouville quantum gravity.
    This FIN diffusions and FK processes are known to be the scaling limits of the Bouchaud trap models, and the two-dimensional Liouville Brownian motion is conjectured to be the scaling limit of simple random walks on random planar maps.
    In the first part of my talk, I will provide a general framework for studying such time changed processes and their discrete approximations in the case when the underlying stochastic process is strongly recurrent, in the sense that it can be described by a resistance form, as introduced by J. Kigami. In particular, this includes the case of Brownian motion on tree-like spaces and low-dimensional self-similar fractals.
    In the second part of my talk, I will discuss heat kernel estimates for (generalized) FIN diffusions and FK processes on metric measure spaces.
    This talk is based on joint works with D. Croydon (Warwick) and B.M. Hambly (Oxford) and with Z.-Q. Chen (Seattle), P. Kim (Seoul) and J. Wang (Fuzhou).

    Codes MSC :
    60J10 - Markov chains (discrete-time Markov processes on discrete state spaces)
    60J35 - Transition functions, generators and resolvents
    60J45 - Probabilistic potential theory
    60J55 - Local time and additive functionals
    60K37 - Processes in random environments

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 08/06/17
      Date de captation : 30/05/17
      Collection : Research talks
      Format : MP4
      Durée : 00:51:59
      Domaine : Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : http://videos.cirm-math.fr/2017-05-30_Kumagai.mp4

    Informations sur la rencontre

    Nom du congrès : Random walks with memory / Marches aléatoires à mémoire
    Organisteurs Congrès : Gantert, Nina ; Ramirez, Alejandro ; Sabot, Christophe ; Tarres, Pierre ; Toth, Balint
    Dates : 29/05/2017 - 02/06/2017
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1566.html

    Citation Data

    DOI : 10.24350/CIRM.V.19179903
    Cite this video as: Kumagai, Takashi (2017). Time changes of stochastic processes: convergence and heat kernel estimates. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19179903
    URI : http://dx.doi.org/10.24350/CIRM.V.19179903

    Voir aussi


    1. Croydon, D.A., Hambly, B.M., Kumagai, T. (2016). Time-changes of stochastic processes associated with resistance forms. <arXiv:1609.02120> - https://arxiv.org/abs/1609.02120