[seminarioDeProbabilidad] Seminario de Probabilidad y Procesos Estocásticos [SESIÓN ESPECIAL]

[María Clara Fittipaldi]

Miércoles 18 de Septiembre a las 13h15,
Auditorio Alfonso Nápoles Gándara
IMATE

Veno Mramor <https://www.turing.ac.uk/people/researchers/veno-mramor>
Department of Statistics, University of Warwick
& The Alan Turing Institute, UK

Nos hablará sobre "Projections and simulation of spherical Brownian motion".
Abstract: We study a process given by the first n coordinates of a Brownian
motion on the unit sphere in the (n+l)-dimensional Euclidean space and
obtain a stochastic differential equation (SDE) it satisfies. The SDE has
non-Lipschitz coefficients but we are able to provide an analysis of
existence and pathwise uniqueness and show that they always hold. The
square of the radial component is a Wright-Fisher diffusion with mutation
and it features in a skew-product decomposition of the projected spherical
Brownian motion. The uniqueness results and the skew-product decomposition
are considered and proved for a more general SDE on the unit ball in the
n-dimensional Euclidean space. The skew-product decomposition suggests a
simulation algorithm for the increments of the spherical Brownian motion
and a simplification reduces it to the simulation of Wright-Fisher
diffusions. We use a recent algorithm for an exact simulation of
Wright-Fisher diffusions given by Jenkins & Spanò (2017) to obtain an
efficient algorithm for the increments of spherical Brownian motion
allowing a wide range of time-steps.

Organizan
Manuel Domínguez de la Iglesia
María Clara Fittipaldi
Arno Siri-Jégousse

Página web:
http://www.matem.unam.mx/~seminarioproba/

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