Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/stochastic-analysis-and-related-topics-on-the-macroscopic-fractal-z03MZLGxIv
References (24)
-
F. Dacosta (2013)
Examples and Applications -
Y. Peres (1996)
Remarks on intersection-equivalence and capacity-equivalenceAnnales De L Institut Henri Poincare-physique Theorique, 64
-
M.T. Barlow (1992)
125Proc. Lond. Math. Soc., 64
-
(1939)
Sur la croissance locale des processus stochastiques homogénes à accroissements indépendants -
D. Khoshnevisan, Yimin Xiao (2003)
Lévy Processes: Capacity and Hausdorff DimensionMathematics eJournal
-
M. Barlow, S. Taylor (1992)
Defining Fractal Subsets of ZdProceedings of The London Mathematical Society, 64
-
S. Port, C. Stone (1971)
Infinitely divisible processes and their potential theory. IAnnales de l'Institut Fourier, 21
-
M. Motoo (1959)
Proof of the law of iterated logarithm through diffusion equationAnnals of the Institute of Statistical Mathematics, 10
-
J. Bertoin (1999)
Subordinators: Examples and ApplicationsLecture Notes in Mathematics
-
D. Khoshnevisan, Yimin Xiao, Yuquan Zhong (2003)
Measuring the range of an additive Lévy processAnnals of Probability, 31
-
J. Seaman (1990)
Introduction to the theory of coverage processesTechnometrics, 32
-
W. Pruitt (1969)
The Hausdorff Dimension of the Range of a Process with Stationary Independent IncrementsIndiana University Mathematics Journal, 19
-
J. Horowitz (1968)
The hausdorff dimension of the sample path of a subordinatorIsrael Journal of Mathematics, 6
-
J. Hawkes (1981)
Trees Generated by a Simple Branching ProcessJournal of The London Mathematical Society-second Series
-
D. Khoshnevisan, Kunwoo Kim, Yimin Xiao (2015)
Intermittency and multifractality: A case study via parabolic stochastic PDEsAnnals of Probability, 45
-
Yimin Xiao (2003)
Random Fractals and Markov ProcessesMathematics eJournal
-
S. Bochner, T. Teichmann (1957)
Harmonic Analysis And The Theory Of Probability -
B. Ripley, P. Hall (1989)
Introduction to the Theory of Coverage Processes.Biometrics, 45
-
H. McKean (1955)
Sample Functions of Stable ProcessesAnnals of Mathematics, 61
-
D. Khoshnevisan, Yimin Xiao (2007)
Harmonic analysis of additive Lévy processesProbability Theory and Related Fields, 145
-
M. Barlow, Stephen Taylor (1989)
Fractional dimension of sets in discrete spacesJournal of Physics A, 22
-
Y. Peres (1996)
Intersection-equivalence of Brownian paths and certain branching processesCommunications in Mathematical Physics, 177
-
Mathematical Proceedings of the Cambridge Philosophical Society The measure theory of random fractals -
M.T. Barlow (1989)
2621J. Phys. A, 22
- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing AG 2017
- ISBN
- 978-3-319-59670-9
- Pages
- 179 –206
- DOI
- 10.1007/978-3-319-59671-6_9
- Publisher site
- See Chapter on Publisher Site
Abstract
[This paper is concerned mainly with the macroscopic fractal behavior of various random sets that arise in modern and classical probability theory. Among other things, it is shown here that the macroscopic behavior of Boolean coverage processes is analogous to the microscopic structure of the Mandelbrot fractal percolation. Other, more technically challenging, results of this paper include: The computation of the macroscopic Minkowski dimension of the graph of a large family of Lévy processes; andThe determination of the macroscopic monofractality of the extreme values of symmetric stable processes.]
Published: Sep 27, 2017
Keywords: Boolean models; Lévy processes; Macroscopic Minkowski dimension; Primary 60G51; Secondary 28A80; 60G17; 60G52