Details
| Original language | English |
|---|---|
| Pages (from-to) | 4587-4612 |
| Number of pages | 26 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 26 |
| Issue number | 8 |
| Early online date | Oct 2020 |
| Publication status | Published - Aug 2021 |
| Externally published | Yes |
Abstract
Building on results obtained in [21], we prove Local Stable and Un- stable Manifold Theorems for nonlinear, singular stochastic delay differential equations. The main tools are rough paths theory and a semi-invertible Multiplicative Ergodic Theorem for cocycles acting on measurable fields of Banach spaces obtained in [20].
Keywords
- Random dynamical systems, Rough paths, Stable and unstable manifolds, Stochastic delay differential equations
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Discrete Mathematics and Combinatorics
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In: Discrete and Continuous Dynamical Systems - Series B, Vol. 26, No. 8, 08.2021, p. 4587-4612.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A dynamical theory for singular stochastic delay differential equations II: Nonlinear equations and invariant manifolds
AU - Ghani Varzaneh, Mazyar
AU - Riedel, Sebastian
N1 - Funding information: Acknowledgments. MGV acknowledges a scholarship from the Berlin Mathematical School (BMS). SR is supported by the MATH+ project AA4-2 Optimal control in energy markets using rough analysis and deep networks. Work on this paper was started while SR was supported by the DFG via Research Unit FOR 2402. Both authors would like to thank M. Scheutzow for valuable discussions and comments during the preparation of the manuscript.
PY - 2021/8
Y1 - 2021/8
N2 - Building on results obtained in [21], we prove Local Stable and Un- stable Manifold Theorems for nonlinear, singular stochastic delay differential equations. The main tools are rough paths theory and a semi-invertible Multiplicative Ergodic Theorem for cocycles acting on measurable fields of Banach spaces obtained in [20].
AB - Building on results obtained in [21], we prove Local Stable and Un- stable Manifold Theorems for nonlinear, singular stochastic delay differential equations. The main tools are rough paths theory and a semi-invertible Multiplicative Ergodic Theorem for cocycles acting on measurable fields of Banach spaces obtained in [20].
KW - Random dynamical systems
KW - Rough paths
KW - Stable and unstable manifolds
KW - Stochastic delay differential equations
UR - http://www.scopus.com/inward/record.url?scp=85108566212&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2003.03202
DO - 10.48550/arXiv.2003.03202
M3 - Article
VL - 26
SP - 4587
EP - 4612
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 8
ER -