Kilian Raschel (Tours)

will speak on

Reflected Brownian motion in a wedge and q-difference equations

Time: 3:00PM
Date: Wed 24th March 2021
Location: Online [map]

Abstract: We consider a semimartingale reflected Brownian motion in a
two-dimensional wedge. Under standard assumptions on the parameters of
the model (opening of the wedge, angles of the reflections on the
axes, drift), we study the algebraic and differential nature of the
Laplace transform of its stationary distribution. We derive necessary
and sufficient conditions for this Laplace transform to be rational,
algebraic, differentially finite or more generally differentially
algebraic. These conditions are explicit linear dependencies among the
angles involved in the definition of the model.

To prove these results, we start from a functional equation that the
Laplace transform satisfies, to which we apply tools from diverse
horizons. To establish differential algebraicity, a key ingredient is
Tutte's invariant approach, which originates in enumerative
combinatorics. To establish differential transcendence, we turn the
functional equation into a difference equation and apply Galoisian
results on the nature of the solutions to such equations.

This is a joint work with M. Bousquet-Mélou, A. Elvey Price, S.
Franceschi and C. Hardouin (https://arxiv.org/abs/2101.01562).

Zoom Link:
https://ucd-ie.zoom.us/j/83491228915?pwd=WWV3ZkNGNzVXdGxLRlR0dkdMYUtMZz09

Meeting ID: 834 9122 8915
Passcode: 698437

(This talk is part of the Probability series.)

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