Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491887
Title: Stochastic flows and sticky Brownian motion
Author: Howitt, Christopher John
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2007
Availability of Full Text:
Access through EThOS:
Access through Institution:
Abstract:
Sticky Brownian motion is a one-dimensional diffusion with the property that the amount of time the process spends at zero is of positive Lebesgue measure and yet the process does not stay at zero for any positive interval of time. Sticky Brownian motion can be considered as qualitatively between standard Brownian motion and Brownian motion absorbed at zero. A system of coalescing Brownian motions is a collection of paths, where each path behaves as a Brownian motion independent of all other paths until the first time two paths meet, at which point the two paths that have just met behave is a single Brownian motion independent of all remaining paths. Thus the difference between any two paths of a system of coalescing Brownian motion behaves as a Brownian motion absorbed at zero. In this thesis we consider systems of Brownian paths, where the difference between any two paths behaves as a sticky Brownian motion rather than a coalescing Brownian motion. We consider systems of sticky Brownian motions starting from points in continuous time and space. The evolution of systems of this type may be described by means of a stochastic flow of kernels. A stochastic flow of kernels is characterised by its N-point motions which form a consistent family of Brownian motions. We characterise such a consistent family such that the difference between any pair of coordinates behaves as a sticky Brownian motion. The Brownian web is a way of describing a system of coalescing Brownian motions starting in any point in space and time. We describe a coupling of Brownian webs such that the difference between one path in each web behaves as a sticky Brownian motion. Then by conditioning one Brownian web on the other we can construct a stochastic flow of kernels. Finally we discuss the concept of duality in relation to flows and we prove some minor results relating to these dualities.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.491887  DOI: Not available
Keywords: QA Mathematics
Share: