Noise-induced transitions for one-dimensional diffusions
作者:
M. Scheutzow,
期刊:
Stochastic Analysis and Applications
(Taylor Available online 1996)
卷期:
Volume 14,
issue 5
页码: 535-563
ISSN:0736-2994
年代: 1996
DOI:10.1080/07362999608809456
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
We consider a one-dimensional diffusion X on a finite or infinite interval]l,r[ satisfying a stochastic differential equationwith W(t) t 0 standard Brownian motion. For fixed drift b we investigate noiseinduced transitions of the boundary behavior i.e. the dependence of the behavior of X near r when σ varies. Particularly we are interested in the question whether increasing σ (for all x) may cause or prevent explosion in finite time. A negative result is that if σ is bounded and bounded away from zero then multiplying σ by a factor greater than one can never prevent explosions (Theorem 2.1). Various examples show that under different assumptions increasing the noise can have a drastic stabilizing or destabilizing effect (depending on b and σ). In the last section we study the relation between the stochastic and deterministic (σ ≡ 0) case
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