Integral expression for the stationary distribution of reflected brownian motion in a wedge
arXiv:1703.09433 · doi:10.3150/19-BEJ1107
Abstract
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 distribution (when it exists), in terms of Cauchy integrals and generalized Chebyshev polyno-mials. To that purpose we solve a Carleman-type boundary value problem on a hyperbola, satisfied by the Laplace transforms of the boundary stationary distribution.
References in corpus (8)
- Intervals in the greedy Tamari posets
- Counting quadrant walks via Tutte's invariant method
- On 3-dimensional lattice walks confined to the positive octant
- On the nature of the generating series of walks in the quarter plane
- Positive recurrence of reflecting Brownian motion in three dimensions
- Tutte's invariant approach for Brownian motion reflected in the quadrant
- A Dirichlet Process Characterization of RBM in a Wedge
- A two-dimensional oblique extension of Bessel processes
Cited by in corpus (10)
- Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant
- Green's Functions with Oblique Neumann Boundary Conditions in the Quadrant
- A dual skew symmetry for transient reflected Brownian motion in an orthant
- Probability of total domination for transient reflecting processes in a quadrant
- Reflecting random walks in curvilinear wedges
- On the stationary distribution of reflected Brownian motion in a wedge: differential properties
- Asymptotics for the Green's functions of a transient reflected Brownian motion in a wedge
- Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity
- Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability
- Stationary Brownian motion in a 3/4-plane: Reduction to a Riemann-Hilbert problem via Fourier transforms