2017/06/21 by Tomoyuki Ichiba, Andrey Sarantsev, Ichiba, Tomoyuki +1
Economics, Econometrics and Finance · Mathematics · #60H10 #60J50 #60J60 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1706.07127
openalex publication_date 2017/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Walsh diffusion on Euclidean space moves along each ray from the origin, as a solution to a stochastic differential equation with certain drift and diffusion coefficients, as long as it stays away from the origin. As it hits the origin, it instantaneously chooses a new direction according to a given probability law, called the spinning measure. A special example is a real-valued diffusion with skew reflections at the origin. This process continuously (in the weak sense) depends on the spinning measure. We determine a stationary measure for such process, explore long-term convergence to this distribution and establish an explicit rate of exponential convergence.