15 citations · 66 across the 15 of their papers we have counts for
16 papers
How to Study Reflected Brownian Motion in a Quadrant via Kernel Functional Equations? A short survey
Sandro Franceschi
We survey a line of works studying semimartingale reflected Brownian motion in a quadrant, covering both the non-degenerate and degenerate settings. Two main situations are emphasi…
On the Green's functions and Martin boundary structure of a planar diffusion in a discontinuous layered medium
Sandro Franceschi, Irina Kourkova, Maxence Petit
We consider a two-dimensional diffusion process in a two-layered plane, governed by distinct covariance matrices in the upper and lower half-planes and by two drift vectors pointed…
Invariant measure of gaps in degenerate competing three-particle systems
Sandro Franceschi, Tomoyuki Ichiba, Ioannis Karatzas +1
We study the gap processes in a degenerate system of three particles interacting through their ranks. We obtain the Laplace transform of the invariant measure of these gaps, and an…
Asymptotics for the Green's functions of a transient reflected Brownian motion in a wedge
Sandro Franceschi, Irina Kourkova, Maxence Petit
We consider a transient Brownian motion reflected obliquely in a two-dimensional wedge. A precise asymptotic expansion of Green's functions is found in all directions. To this end,…
A dual skew symmetry for transient reflected Brownian motion in an orthant
Sandro Franceschi, Kilian Raschel
We introduce a transient reflected Brownian motion in a multidimensional orthant, which is either absorbed at the apex of the cone or escapes to infinity. We address the question o…
Stationary Brownian motion in a 3/4-plane: Reduction to a Riemann-Hilbert problem via Fourier transforms
Guy Fayolle, Sandro Franceschi, Kilian Raschel
The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In…
On the stationary distribution of reflected Brownian motion in a non-convex wedge
Guy Fayolle, Sandro Franceschi, Kilian Raschel
We study the stationary reflected Brownian motion in a non-convex wedge, which, compared to its convex analogue model, has been much rarely analyzed in the probabilistic literature…
On the stationary distribution of reflected Brownian motion in a wedge: differential properties
M. Bousquet-Mélou, A. Elvey Price, S. Franceschi +2
We consider the classical problem of determining the stationary distribution of the semimartingale reflected Brownian motion (SRBM) in a two-dimensional wedge. Under standard assum…
Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant
Philip Ernst, Sandro Franceschi, Dongzhou Huang
We consider an obliquely reflected Brownian motion with positive drift in a quadrant stopped at time , where is the first hitting time of th…
Probability of total domination for transient reflecting processes in a quadrant
Vladimir Fomichov, Sandro Franceschi, Jevgenijs Ivanovs
We consider two-dimensional Lévy processes reflected to stay in the positive quadrant. Our focus is on the non-standard regime when the mean of the free process is negative but the…
Asymptotic behavior of the occupancy density for obliquely reflected Brownian motion in a half-plane and Martin boundary
Philip Ernst, Sandro Franceschi
Let be the occupancy density of an obliquely reflected Brownian motion in the half plane and let (, ) be the polar coordinates of a point in the upper half plane. This wo…
Green's Functions with Oblique Neumann Boundary Conditions in the Quadrant
Sandro Franceschi
We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit inte…
Integral expression for the stationary distribution of reflected brownian motion in a wedge
Sandro Franceschi, Kilian Raschel
For Brownian motion in a (two-dimensional) wedge with negative drift and oblique reflection on the axes, we derive an explicit formula for the Laplace transform of its stationary d…
Analytic approach for reflected Brownian motion in the quadrant
Sandro Franceschi, Irina Kourkova, Kilian Raschel
Random walks in the quarter plane are an important object both of combinatorics and probability theory. Of particular interest for their study, there is an analytic approach initia…
Asymptotic expansion of stationary distribution for reflected Brownian motion in the quarter plane via analytic approach
Sandro Franceschi, Irina Kourkova
Brownian motion in R 2 + with covariance matrix and drift in the interior and reflection matrix R from the axes is considered. The asymptotic expansion of the stationary di…
Tutte's invariant approach for Brownian motion reflected in the quadrant
Sandro Franceschi, Kilian Raschel
We consider a Brownian motion with drift in the quarter plane with orthogonal reflection on the axes. The Laplace transform of its stationary distribution satisfies a functional eq…