A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs
SCIE
SCOPUS
- Title
- A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs
- Authors
- Khoshnevisan, Davar; Kim, Kunwoo; Xiao, Yimin
- Date Issued
- 2018-05
- Publisher
- SPRINGER
- Abstract
- It is generally argued that the solution to a stochastic PDE with multiplicative noise-such as , where denotes space-time white noise-routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (Arch Ration Mech Anal 177:115-150, 2005), Gibbon and Titi (Proc R Soc A 461:3089-3097, 2005), and Zimmermann et al. (Phys Rev Lett 85(17):3612-3615, 2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (J Phys A 22(13):2621-2626, 1989; Proc Lond Math Soc (3) 64:125-152, 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/94688
- DOI
- 10.1007/s00220-018-3136-6
- ISSN
- 0010-3616
- Article Type
- Article
- Citation
- COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 360, no. 1, page. 307 - 346, 2018-05
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