Brownian motion in a closed convex polygon with normal reflection

Motion Planning for a Convex Polygon in a Polygonal Environment

We study the motion-planning problem for a convex m-gon P in a planar polygonal environment Q bounded by n edges. We give the rst algorithm that constructs the entire free connguration space (the 3-dimensional space of all free placements of P in Q) in time that is near-quadratic in mn, which is nearly optimal in the worst case. The algorithm is also conceptually relatively simple. Previous sol...

Brownian motion, reflection groups and Tanaka formula

In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka’s formula for linear Brownian motion. The paper is closed with a description of the boun...

Finding the Maximum Area Centrosymmetric Polygon in a Convex Polygon

Integration in a Normal World: Fractional Brownian Motion and Beyond

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Lauri Viitasaari Name of the doctoral dissertation Integration in a Normal World: Fractional Brownian Motion and Beyond Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 14/2014 Field of research Mathematics Manuscript submitted 12 ...

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory