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Imagine a Brownian crook who spent a month in a large metropolis. The number of nights he spent in hotels A,B,C...etc. is known; but not the order, nor his itinerary. So the only information the police has is total hotel bills..... Let ? W t ; t 0 be reeecting Brownian motion issuing from zero, and let l(t; y), for y 2 R + and t 0, denote the local time… (More)
In this paper, we consider trading with proportional transaction costs as in Schachermayer's paper of 2004. We give a necessary and sufficient condition for A, the cone of claims attainable from zero endowment, to be closed. Then we show how to define a revised set of trading prices in such a way that firstly, the corresponding cone of claims attainable for… (More)
A family of reflected Brownian motions is used to construct Dyson's process of non-colliding Brownian motions. A number of explicit formulae are given, including one for the distribution of a family of coalescing Brownian motions.
We give examples of stochastic processes in the Gelfand Tsetlin cone in which each component evolves independently apart from a blocking and pushing interaction. The processes give couplings to certain conditioned Markov processes, last passage times and asymetric exclusion processes. An example of a cone valued process whose components cannot escape past a… (More)
In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of these orders in terms of a class of generalized riffle shuffles.
The law of a random tree constructed within a Brownian excursion is calculated conditional on knowing the occupation measure of the excursion. In previous work David Aldous has used random walk approximations to obtain this result. Here it is deduced from Le Gall's description of the tree in the unconditioned excursion.
For a wide class of stationary subdivision methods, we derive necessary and suucient conditions for these schemes to produce C k continuous limit curves. These stationary schemes include those arising from midpoint subdivision of irregularly-spaced knot sequences. We also describe a matrix method for computing various derivative schemes associated with such… (More)
The purpose of this article is to study a coalescing flow of sticky Brownian motions on [0, ∞). Sticky Brownian motion arises as the weak solution of a stochastic differential equation, and the study of flow reveals the nature of the extra randomness that must be added to the driving Brownian motion. This can be represented in terms of Poissonian marking of… (More)
A fundamental problem in geometry processing is that of expressing a point inside a convex polyhedron as a combination of the vertices of the polyhedron. Instances of this problem arise often in mesh parameterization and 3D deformation. A related problem is to express a vector lying in a convex cone as a non-negative combination of edge rays of this cone.… (More)
Consider the following mechanism for the random evolution of a distribution of mass on the integer lattice Z. At unit rate, independently for each site, the mass at the site is split into two parts by choosing a random proportion distributed according to some specified probability measure on [0, 1] and dividing the mass in that proportion. One part then… (More)