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A practical criterion for positivity of transition densities

dc.contributor.author Herzog, David P
dc.contributor.author Mattingly, Jonathan Christopher
dc.date.accessioned 2015-03-20T17:39:11Z
dc.date.issued 2015-07-10
dc.identifier.issn 0951-7715
dc.identifier.uri http://hdl.handle.net/10161/9510
dc.description.abstract © 2015 IOP Publishing Ltd & London Mathematical Society.We establish a simple criterion for locating points where the transition density of a degenerate diffusion is strictly positive. Throughout, we assume that the diffusion satisfies a stochastic differential equation (SDE) on Rd with additive noise and polynomial drift. In this setting, we will see that it is often the case that local information of the flow, e.g. the Lie algebra generated by the vector fields defining the SDE at a point x ∈ Rd, determines where the transition density is strictly positive. This is surprising in that positivity is a more global property of the diffusion. This work primarily builds on and combines the ideas of Arous and Lé andre (1991 Décroissance exponentielle du noyau de la chaleur sur la diagonale. II Probab. Theory Relat. Fields 90 377-402) and Jurdjevic and Kupka (1985 Polynomial control systems Math. Ann. 272 361-8).
dc.relation.ispartof Nonlinearity
dc.relation.isversionof 10.1088/0951-7715/28/8/2823
dc.title A practical criterion for positivity of transition densities
dc.type Journal article
pubs.begin-page 2823
pubs.end-page 2845
pubs.issue 8
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Statistical Science
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Published
pubs.volume 28
dc.identifier.eissn 1361-6544


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