Asymptotic Distributions for Power Variations of the Solutions to Linearized Kuramoto–Sivashinsky SPDEs in One-to-Three Dimensions
Abstract
:1. Introduction
2. Statement of Results
2.1. Exact Convergence Rates of Variances and Temporal CLTs for the Realized Power Variations of LKS-SPDEs
2.2. Exact Convergence Rates of Variances and Temporal CLTs for the Realized Power Variations of LKS-SPDE Gradient
3. Methodology
3.1. Rigorous Kernel Stochastic Integral Equations Formulations
3.2. Estimates on the Temporal Increments of LKS-SPDEs and Their Gradient
4. Results
4.1. Exact Convergence Rates of Variances for LKS-SPDEs
4.2. Temporal CLTs for LKS-SPDEs
- (a)
- , and
- (b)
- for all ,
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
SPDE | Stochastic partial differential equation |
LKS | Linearized Kuramoto–Sivashinsky |
SIE | Stochastic integral equation |
FBM | fractional Brownian motion |
BBM | bifractional Brownian motion |
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Wang, W.; Wang, D. Asymptotic Distributions for Power Variations of the Solutions to Linearized Kuramoto–Sivashinsky SPDEs in One-to-Three Dimensions. Symmetry 2021, 13, 73. https://doi.org/10.3390/sym13010073
Wang W, Wang D. Asymptotic Distributions for Power Variations of the Solutions to Linearized Kuramoto–Sivashinsky SPDEs in One-to-Three Dimensions. Symmetry. 2021; 13(1):73. https://doi.org/10.3390/sym13010073
Chicago/Turabian StyleWang, Wensheng, and Dazhong Wang. 2021. "Asymptotic Distributions for Power Variations of the Solutions to Linearized Kuramoto–Sivashinsky SPDEs in One-to-Three Dimensions" Symmetry 13, no. 1: 73. https://doi.org/10.3390/sym13010073
APA StyleWang, W., & Wang, D. (2021). Asymptotic Distributions for Power Variations of the Solutions to Linearized Kuramoto–Sivashinsky SPDEs in One-to-Three Dimensions. Symmetry, 13(1), 73. https://doi.org/10.3390/sym13010073