Abstract
The objective of this paper is to use the Lyapunov function to study the almost sure exponential stability of the stochastic differential equation Φt = x + ∫0t F(Φs, ds), where F(x, t) is a continuous C-semimartingale with spatial parameter x. This equation includes many important stochastic systems, for example, the classical Ito equation. More importantly, the result can be employed to study the bound of the Lyapunov exponent of stochastic flows.
Original language | English |
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Pages (from-to) | 1481-1490 |
Number of pages | 10 |
Journal | SIAM Journal on Control and Optimization |
Volume | 28 |
Issue number | 6 |
DOIs | |
Publication status | Published - 1 Nov 1990 |
Keywords
- mathematical methods
- differential equations
- exponential stability
- Lyapunov functions
- stochastic differential equations
- system stability
- riccati equation
- sensitivity
- stabilizability
- computable bonds