[SeminarioDeProbabilidad] Seminario de Probabilidad y Procesos Estocásticos - 28 de septiembre de 2022

[María Clara Fittipaldi]

*Fecha*: Miércoles 28 de septiembre de 2022 a las 13h15.
*Lugar*:   Auditorio Alfonso Nápoles Gándara, Instituto de Matemáticas.

*Expositor*: Sebastian Hummel
<https://statistics.berkeley.edu/people/sebastian-hummel>
Department of Statistics
University of California, Berkeley.

*Título*: "Boundary behavior of the Λ-Wright--Fisher process with selection"
*Abstract*: Λ-Wright--Fisher processes provide an important modeling
framework within mathematical population genetics. We present a variety of
parameter-dependent long-term behaviors for a broad class of such processes
and explain how to discriminate the different boundary behaviors by
explicit criteria. In particular, we describe situations in which both
boundary points are asymptotically inaccessible – an apparently new
phenomenon in this context. This has interesting biological implications,
because it leads to a class of stochastic population models in which
selection alone can maintain genetic variation. If at least one boundary
point is asymptotically accessible, we derive decay rates for the
probability that the boundary is not essentially accessed. To prove this
result, we establish and employ Siegmund duality. The dual process can be
sandwiched at the boundary in between two transformed Lévy processes. This
allows us to relate the boundary behavior of the dual to fluctuation
properties of the Lévy processes and it sheds new light on previously
established accessibility conditions. This is joint work with Fernando
Cordero and Grégoire Véchambre.
Organizan
Laura Eslava
María Clara Fittipaldi
Saraí Hernández-Torres.

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