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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)
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)