Integral expression for the stationary distribution of reflected Brownian motion in a wedge
Integral expression for the stationary distribution of reflected Brownian motion in a wedge
复制标题
楔块反射布朗运动平稳分布的积分表达式
作者：
S. Franceschi;K. Raschel
对于具有负漂移和轴上斜反射的(二维)楔体中的布朗运动，我们用柯西积分和广义切比雪夫多项式导出了其平稳分布(当存在时)的拉普拉斯变换的显式公式。为此，我们解决了双曲线上的Carleman边值问题，满足边界平稳分布的拉普拉斯变换。
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.