Abstract
A new sufficient condition for stability in distribution of a hybrid stochastic delay differential equation (SDDE) has been proposed. In the new criterion leading to stability for an SDDE, its main component only depends on the coefficients of a corresponding SDE without delay. The Lyapunov method is applied to find an upper bound, so that the SDDE is stable in distribution if the delay is less than the upper bound. Also, the criterion shows that delay terms can be impetuses toward the stability in distribution.
| Original language | English |
|---|---|
| Article number | 107169 |
| Journal | Journal of the Franklin Institute |
| Volume | 361 |
| Issue number | 16 |
| Early online date | 12 Aug 2024 |
| DOIs | |
| Publication status | Published - Nov 2024 |
Funding
Xuerong Mao would like to thank the Royal Society(WM160014, Royal Society Wolfson Research Merit Award), the Royal Society and the Newton Fund (NA160317, Royal Society Newton Advanced Fellowship), the Royal Society of Edinburgh(RSE1832), and Shanghai Administration of Foreign Experts Affairs (21WZ2503700, the Foreign Expert Program) for their financial supports.
Keywords
- hybrid stochastic delay differential equations
- Brownian motion
- delay-dependent
- stability in distribution