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Wong-Zakai type approximations of rough random dynamical systems by smooth noise.
- Source :
-
Journal of Differential Equations . Jun2023, Vol. 358, p218-255. 38p. - Publication Year :
- 2023
-
Abstract
- This paper is devoted to the smooth and stationary Wong-Zakai approximations for a class of rough differential equations driven by a geometric fractional Brownian rough path ω with Hurst index H ∈ (1 3 , 1 2 ]. We first construct the approximation ω δ of ω by probabilistic arguments, and then use the rough path theory to obtain the Wong-Zakai approximation for the solution on any finite interval. Finally, both the original system and the approximative system generate a continuous random dynamical systems φ and φ δ. As a consequence of the Wong-Zakai approximation of the solution, φ δ converges to φ as δ → 0. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RANDOM dynamical systems
*BROWNIAN motion
*DIFFERENTIAL equations
*NOISE
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 358
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 162890925
- Full Text :
- https://doi.org/10.1016/j.jde.2023.02.031