Bifurcations of One-Dimensional Stochastic Differential Equations

Hans Crauel, Peter Imkeller and Marcus Steinkamp

Chapter 2 in Stochastic Dynamics, 1999, pp 27-47 from Springer

Abstract: Abstract We consider families of random dynamical systems induced by parametrized one-dimensional stochastic differential equations. We give necessary and sufficient conditions on the invariant measures of the associated Markov semigroups which ensure a stochastic bifurcation. This leads to sufficient conditions on drift and diffusion coefficients for a stochastic pitchfork and transcritical bifurcation of the family of random dynamical systems.

Keywords: Lyapunov Exponent; Invariant Measure; Stochastic Differential Equation; Speed Measure; Invariant Probability Measure (search for similar items in EconPapers)
Date: 1999
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-22655-2_2

Ordering information: This item can be ordered from
http://www.springer.com/9780387226552

DOI: 10.1007/0-387-22655-9_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().