Tohoku Mathematical Journal
2001
March
SECOND SERIES VOL. 53, NO. 1

Tohoku Math. J.
53 (2001), 81-93

Title MOMENT DECAY RATES OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS

Author Kai Liu and Anyue Chen

(Received April 27, 1999)
Abstract. The objective of this paper is to investigate the $p$-th moment asymptotic stability decay rates for certain finite-dimensional Ito stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

2000 Mathematics Subject Classification. Primary 93E03; Secondary 60H10.

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