Laws of the iterated logarithm for some symmetric diffusion processes

Osaka Journal of Mathematics

Volumn 37, Issue 3, 2000, Pages 625-650

  Bass, Richard F ^a   Kumagai, Takashi ^b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005348493     PISSN: 00306126     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. D.G. Aronson: Bounds on the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc. 73 (1967), 890-896.
2. M.T. Barlow: Diffusions on fractals, Lectures in Probability Theory and Statistics: Ecole d'été de probabilités de Saint-Flour XXV, Springer, New York, 1998.
3. M.T. Barlow and R.F. Bass: Construction of Brownian motion on the Sierpinski carpet, Ann. Inst. H. Poincaré, 25 (1989), 225-257.
4. M.T. Barlow and R.F. Bass: Local times for Brownian motion on the Sierpinski carpet, Probab. Theory Relat. Fields, 85 (1990), 91-104.
5. M.T. Barlow and R.F. Bass: Transition densities for Brownian motion on the Sierpinski carpet, Probab. Theory Relat. Fields, 91 (1992), 307-330.
6. M.T. Barlow and R.F. Bass: Brownian motion and harmonic analysis on Sierpinski carpets, Canadian Journal of Math. 51 (1999), 673-744.
7. M.T. Barlow and E.A. Perkins: Brownian motion on the Sierpinski gasket, Probab. Theory Relat. Fields, 79 (1988), 543-624.
8. p inequalities for functionals of Brownian motion, Séminaire de Probabilités XXI, Springer, New York (1987), 206-217.
9. R.F. Bass and D. Khoshnevisan: Local times on curves and uniform invariance principles, Probab. Theory Relat. Fields, 92 (1992), 465-492.
10. G. Ben Arous and T. Kumagai: Large deviations for Brownian motion on the Sierpinski gasket, Stoch. Proc. Their Appl. 85 (2000), 225-235.
11. J. Bertoin: Lévy processes, Cambridge Univ. Press, Cambridge, 1996.
12. K.L. Chung: On the maximum partial sums of sequences of independent random variables, Trans. Amer. Math. Soc. 64 (1948), 205-233.
13. E.B. Fabes and D.W. Stroock: A new proof of Moser's parabolic Harnack inequality via the old ideas of Nash, Arch. Mech. Rat. Anal. 96 (1986), 327-338.
14. P.J. Fitzsimmons, B.M. Hambly and T. Kumagai: Transition density estimates for Brownian motion on affine nested fractals, Commun. Math. Phys. 165 (1994), 595-62.
15. M. Fukushima: Dirichlet forms, diffusion processes and spectral dimensions for nested fractals, In: Ideas and Methods in Mathematical Analysis, Stochastics, and Applications, In Memory of R. Høegh-Krohn, vol. 1 (Albeverio, Fenstad, Holden and Lindstrøm (eds.)), Cambridge Univ. Press, Cambridge (1992), 151-161.
16. M. Fukushima, T. Shima and M. Takeda: Large deviations and related LIL's for Brownian motions on nested fractals, Osaka J. Math. 36 (1999), 497-537.
17. P.S. Griffin: Laws of the iterated logarithm for symmetric stable processes, Z. Wahrsch. verw. Gebiete, 68 (1985), 271-285.
18. J. Kigami: Harmonic calculus on limits of networks and its application to dendrites, J. Funct. Anal. 128 (1995), 48-86.
19. T. Kumagai: Estimates of transition densities for Brownian motion on nested fractals, Probab. Theory Relat. Fields, 96 (1993), 205-224.
20. T. Kumagai: Short time asymptotic behavior and large deviations for Brownian motion on some affine nested fractals, Publ. RIMS. Kyoto Univ. 33-2 (1997), 223-240.
21. S. Kusuoka: Diffusion processes on nested fractals, In: R.L. Dobrushin and S. Kusuoka: Statistical Mechanics and Fractals (Lect. Notes Math., vol. 1567), Springer, New York, 1993.
22. S. Kusuoka and X.Y. Zhou: Dirichlet forms on fractals: Poincaré constant and resistance, Probab. Theory Relat. Fields, 93 (1992), 169-196.
23. T. Lindstrøm: Brownian motion on nested fractals, Memoirs Amer. Math. Soc. 420 83, 1990.
24. M. Schilder: On a Laplace asymptotic formula for Wiener integrals, Trans. Amer. Math. Soc. 125 (1966), 63-85.
25. D.W. Stroock: An Introduction to the Theory of Large Deviations, Springer, New York, 1984.
26. S. Varadhan: On the behavior of the fundamental solution of the heat equation with variable coefficients, Commun. Pure Appl. Math. 20 (1967), 431-455.
27. S. Varadhan: Diffusion processes in a small time interval, Commun. Pure Appl. Math. 20 (1967), 659-685.
28. S. Varadhan: Lectures on diffusion problems and partial differential equations, Tata Institute of Fundamental Research, 1980.
29. I.-S. Wee: The law of the iterated logarithm for local time of a Lévy process, Probab.Theory Relat. Fields, 93 (1992), 359-376.