Abstract
Linear time-varying stochastic differential equations with a.s. convergent continuous random system matrix processes are considered. It is shown that given the limit is known to be Hurwitz (i.e. asymptotically stable), the generated state solutions are a.s. bounded. This property is shown to hold by substantiating that, w.p.1, (i) no finite escape time exists and (ii) no divergence to infinity, as (Formula presented.), may occur. An application to stochastic adaptive control is provided.
| Original language | English |
|---|---|
| Pages (from-to) | 857-867 |
| Number of pages | 11 |
| Journal | Stochastics |
| Volume | 93 |
| Issue number | 6 |
| DOIs | |
| State | Published - 1 Jan 2021 |
Keywords
- 60G17
- 60G44
- 93E03
- 93E15
- 93E35
- Linear stochastic differential equations
- Lyapunov methodology
- positive supermartingale maximal inequality
- sample path boundedness
- stochastic linear quadratic adaptive control
- stochastic system stability
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation