PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Transition Density Estimates for Relativistic α-Stable Processes on Metric Spaces

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove matching upper and lower bounds for the transition density of relativistic α-stable processes on a d-set (F; p; μ); obtained via subordination. We also identify the corresponding Dirichlet form.
Rocznik
Strony
183--204
Opis fizyczny
Bibliogr. 45 poz.
Twórcy
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
  • [1] M. T. Barlow, Diffusions on fractals, in: École d’Été de Probabilité de St. Flour XXV—1995, Lecture Notes in Math. 1690, Springer, Berlin, 1998, 1-121.
  • [2] M. T. Barlow and R. F. Bass, The construction of Brownian motion on the Sierpiński carpet, Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), 225-257.
  • [3] M. T. Barlow and R. F. Bass, Brownian motion and harmonic analysis on Sierpiński carpets, Canad. J. Math. 51 (1999), 673-744.
  • [4] M. T. Barlow, R. F. Bass, T. Kumagai, and A. Teplyaev, Uniqueness of Brownian motion on Sierpiński carpets, J. Eur. Math. Soc. 12 (2010), 655-701.
  • [5] M. T. Barlow and E. A. Perkins, Brownian motion on the Sierpiński gasket, Probab. Theory Related Fields 79 (1988), 543-623.
  • [6] J. Bertoin, Lévy Processes, Cambridge Univ. Press, Cambridge, 1996.
  • [7] J. Bertoin, Subordinators: examples and applications, in: École d’Été de Probabilités de St. Flour XXVII, P. Bernard (ed.), Lecture Notes in Math. 1717, Springer, 1999, 4-79.
  • [8] S. Bochner, Diffusion equation and stochastic processes, Proc. Nat. Acad. Sci. USA 35 (1949), 368-370.
  • [9] S. Bochner, Harmonic Analysis and the Theory of Probability, Univ. of California Press, Berkeley, CA, 1955.
  • [10] K. Bogdan et al., Potential Analysis of Stable Processes and its Extensions (ed. by P. Graczyk and A. Stós), Lecture Notes in Math. 1980, Springer, Berlin, 2009.
  • [11] K. Bogdan, A. Stós, and P. Sztonyk, Harnack inequality for stable processes on d-sets, Studia Math. 158 (2003), 163-198.
  • [12] E. A. Carlen, S. Kusuoka, and D. W. Stroock, Upper bounds for symmetric Markov transition functions, Ann. Inst. H. Poincaré Probab. Statist. 23 (1987), 245-287.
  • [13] R. Carmona, W. C. Masters, and B. Simon, Relativistic Schrödinger operators: Asymptotic behaviour of the eigenfunctions, J. Funct. Anal. 91 (1990), 117-142.
  • [14] Z.-Q. Chen and T. Kumagai, Heat kernel estimates for stable-like processes on d-sets, Stoch. Processes Appl. 108 (2003), 27-62.
  • [15] Z.-Q. Chen and T. Kumagai, Heat kernel estimates for jump processes of mixed types on metric measure spaces, Probab. Theory Related Fields 140 (2008), 277-317.
  • [16] W. Farkas and N. Jacob, Sobolev spaces on non-smooth domains and Dirichlet forms related to subordinate reflecting diffusions, Math. Nachr. 224 (2001), 75-104.
  • [17] M. Fukushima, Dirichlet forms, diffusion processes, and spectral dimensions for nested fractals, in: Ideas and Methods in Mathematical Analysis, Stochastics, and Applications (Oslo, 1988), Cambridge Univ. Press., Cambridge, 1992, 151-161.
  • [18] M. Fukushima, Y. Oshima, and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, de Gruyter, Berlin, 1994.
  • [19] A. Grigor’yan, Heat kernels and function theory on metric measure spaces, in: Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces (Paris, 2002), Contemp. Math. 338, Amer. Math. Soc., Providence, RI, 2003, 143-172.
  • [20] A. Grigor’yan, H. Hu, and K.-S. Lau, Heat kernels on metric measure spaces and an application to semilinear elliptic equations, Trans. Amer. Math. Soc. 355 (2003), 2065-2095.
  • [21] S. Havlin and D. Ben-Avraham, Diffusion in disordered media, Adv. Phys. 36 (1987), 695-798.
  • [22] J. Hawkes, A lower Lipschitz condition for the stable subordinator, Z. Wahrsch. Verw. Gebiete 17 (1971), 23-32.
  • [23] M. Hino and T. Kumagai, A trace theorem for Dirichlet forms on fractals, J. Funct. Anal. 238 (2006), 578-611.
  • [24] J. Hu and M. Zähle, Potential spaces on fractals, Studia Math. 170 (2005), 259-281.
  • [25] J. Hu and M. Zähle, Generalized Bessel and Riesz potentials on metric measure spaces, Potential Anal. 30 (2009), 315-340.
  • [26] N. Jacob and R. Schilling, Some Dirichlet spaces obtained by subordinate reflected diffusions, Rev. Mat. Iberoamer. 15 (1999), 59-91.
  • [27] A. Jonsson, Brownian motion on fractals and function spaces, Math. Z. 222 (1996), 495-504.
  • [28] A. Jonsson, A trace theorem for the Dirichlet form on the Sierpinski gasket, Math. Z. 250 (2005), 599-609.
  • [29] A. Jonsson and H. Wallin, Function Spaces on Subsets of Rn, Math. Reports 2, Part 1, Harwood, 1984.
  • [30] K. Kaleta and P. Sztonyk, Small-time sharp bounds for kernels of convolution semigroups, J. Anal. Math. 132 (2017), 355-394.
  • [31] P. Kim and A. Mimica, Green function estimates for subordinate Brownian motions: stable and beyond, Trans. Amer. Math. Soc. 366 (2014), 4383-4422.
  • [32] T. Kulczycki and B. Siudeja, Intrinsic ulrtacontractivity of the Feynman-Kac semigroup for relativistic stable processes, Trans. Amer. Math. Soc. 358 (2006), 5025-5057.
  • [33] T. Kumagai, Estimates on transition densities for Brownian motion on nested fractals, Probab. Theory Related Fields 96 (1993), 205-224.
  • [34] T. Kumagai, Function spaces and stochastic processes on fractals, in: Fractal Geometry and Stochastics III, Progr. Probab. 57, Birkhäuser, Basel, 2004, 221-234.
  • [35] E. H. Lieb and R. Seiringer, The Stability of Matter in Quantum Mechanics, Cambridge Univ. Press, 2009.
  • [36] T. Lindstrøm, Brownian motion on nested fractals, Mem. Amer. Math. Soc. 83 (1990), no. 420, iv + 128 pp.
  • [37] K. Pietruska-Pałuba, On function spaces related to the fractional diffusions on d-sets, Stoch. Stoch. Reports 70 (2000), 153-164.
  • [38] M. Ryznar, Estimates of Green function for relativistic _-stable process, Potential Anal. 17 (2002), 1-23.
  • [39] C. Sabot, Existence and uniqueness of diffusions on finitely ramified self-similar fractals, Ann. Sci. École Norm. Sup. (4) 30 (1997), 605-673.
  • [40] R. Schilling, R. Song and Z. Vondraček, Bernstein Functions. Theory and Applications, de Gruyter Stud. Math. 37, de Gruyter, Berlin, 2010.
  • [41] R. Schilling and J. Wang, Functional inequalities and subordination: stability of Nash and Poincaré inequalities, Math. Z. 272 (2012), 921-936.
  • [42] A. Stós, Symmetric α-stable processes on d-sets, Bull. Polish Acad. Sci. Math. 48 (2000), 237-245.
  • [43] K.-T. Sturm, Diffusion processes and heat kernels on metric spaces, Ann. Probab. 26 (1998), 1-55.
  • [44] H. Triebel, Theory of Function Spaces. III, Monogr. Math. 100, Birkhäuser, Basel, 2006.
  • [45] H. Triebel, Fractals and Spectra Related to Fourier Analysis and Function Spaces, Modern Birkhäuser Classics, Birkhäuser, Basel, 2011.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f0cb9a0a-8f9d-4720-97ce-70fc6369b1b3
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.