Abstract
Our goal is to relax a sufficient condition for the exponential almost sure stability
of a certain class of stochastic differential equations. Compare to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose.
of a certain class of stochastic differential equations. Compare to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose.
| Original language | English |
|---|---|
| Pages (from-to) | 221-227 |
| Number of pages | 7 |
| Journal | Bulletin of the Korean Mathematical Society |
| Volume | 51 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2014 |
Keywords
- almost sure stability
- Bessel squared process
- Stochastic differential equations
- regime-switching system
- Lipschitz continuity