### Abstract

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.

Language | English |
---|---|

Pages | 221-227 |

Number of pages | 7 |

Journal | Bulletin of the Korean Mathematical Society |

Volume | 51 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2014 |

### Fingerprint

### Keywords

- almost sure stability
- Bessel squared process
- Stochastic differential equations
- regime-switching system
- Lipschitz continuity

### Cite this

*Bulletin of the Korean Mathematical Society*,

*51*(1), 221-227. https://doi.org/10.4134/BKMS.2014.51.1.221

}

*Bulletin of the Korean Mathematical Society*, vol. 51, no. 1, pp. 221-227. https://doi.org/10.4134/BKMS.2014.51.1.221

**A note on exponential almost sure stability of stochastic differential equation.** / Mao, Xuerong; Song, Qingshuo; Yang, Dichuan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A note on exponential almost sure stability of stochastic differential equation

AU - Mao, Xuerong

AU - Song, Qingshuo

AU - Yang, Dichuan

PY - 2014/1

Y1 - 2014/1

N2 - Our goal is to relax a sufficient condition for the exponential almost sure stabilityof 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.

AB - Our goal is to relax a sufficient condition for the exponential almost sure stabilityof 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.

KW - almost sure stability

KW - Bessel squared process

KW - Stochastic differential equations

KW - regime-switching system

KW - Lipschitz continuity

UR - http://bkms.kms.or.kr/

U2 - 10.4134/BKMS.2014.51.1.221

DO - 10.4134/BKMS.2014.51.1.221

M3 - Article

VL - 51

SP - 221

EP - 227

JO - Bulletin of the Korean Mathematical Society

T2 - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

SN - 1015-8634

IS - 1

ER -