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Probability and Computational Finance Seminar
Soumik Pal University of Washington Title: Brownian particles with asymmetric collisions Abstract: Imagine a collection of particles on the line performing random motion while preserving their order. When two particles collide, classical models assume elastic collision. Informally, if these movements are modeled by Brownian motions, the key stochastic feature of elastic collision is the equal division of the `local time' push among the two colliding particles. However an array of useful particle models behave asymmetrically. A well-known example is the Totally Asymmetric Exclusion Process. We consider such discrete models of particle movements on the line with asymmetric collisions. We show that their scaling limits are given by colliding Brownian particles whose local time of collision is distributed unequally among the members. An interesting component of the analysis is a generalization of Skorokhod maps in this context. The limiting continuous processes correct several features of the \textit{first order models} in stochastic portfolio theory to conform more with available data. Based on joint work with Ioannis Karatzas and Mykhaylo Shkolnikov.Date: Thursday, October 25, 2012Time: 5:00 pmLocation: Wean Hall 6423Submitted by: ShreveNote: this seminar is on THURSDAY. |