Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1060.60059
Appleby, John A.D.; Kelly, Cónall
Oscillation and non-oscillation in solutions of nonlinear stochastic delay differential equations. (English)
[J] Electron. Commun. Probab. 9, 106-118, electronic only (2004). ISSN 1083-589X/e

Summary: This paper studies the oscillation and non-oscillation of solutions of a nonlinear stochastic delay differential equation, where the noise perturbation depends on the current state, and the drift depends on a delayed argument. When the restoring force towards equilibrium is relatively strong, all solutions oscillate, almost surely. However, if the restoring force is superlinear, positive solutions exist with positive probability, and for suitably chosen initial conditions, the probability of positive solutions can be made arbitrarily close to unity.

MSC 2000:: *60H10 Stochastic ordinary differential equations
34K11 Oscillation theory of functional-differential equations
34K50 Stochastic delay equations

Keywords: stochastic delay differential equation; oscillation; non-oscillation

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]