Geometrical optics of constrained Brownian motion: three short stories

Exact geometrical optics and analytical investigations on motion

Frank Grave, 2, ∗ Michael Buser, Thomas Müller, Günter Wunner, and Wolfgang P. Schleich 1 1. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57 // IV, 70550 Stuttgart, Germany Visualisierungsinstitut der Universität Stuttgart, Universität Stuttgart, Nobelstraße 15, D-70569 Stuttgart, Germany Institut für Quantenphysik, Universität Ulm, D-89069 Ulm, Germany (Dated: Octob...

Short Timescale Effects in Brownian Motion

To my beautiful family, for all the help they have given me.

Brownian motion in short range random potentials

A. H. Romero and J. M. Sancho Department of Physics, University of California, San Diego, La Jolla, California 92093-0354 Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093-0340 Institute for Nonlinear Science, Department 0407, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0407 and Departament d’Estructu...

Brownian motion at short time scales

Impulse Control of Brownian Motion: The Constrained Average Cost Case

When a manufacturer places repeated orders with a supplier to meet changing production requirements, he faces the challenge of finding the right balance between holding costs and the operational costs involved in adjusting the shipment sizes. We consider an inventory whose content fluctuates as a Brownian motion in the absence of control. At any moment, a controller can adjust the inventory lev...