2012/03/19 by Hatem Hajri, Hajri, Hatem, Olivier Raimond +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1203.4048
To appear in ALEA Lat. Am. J. Probab. Math. Stat
openalex publication_date 2012/03/19 · arxiv created 2013/04/21 · arxiv updated 2013/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a Tanaka's equation on an oriented graph with two edges and two vertices. This graph will be embedded in the unit circle. Extending this equation to flows of kernels, we show that the laws of the flows of kernels K solution of Tanaka's equation can be classified by pairs of probability measures (m+,m-) on [0,1], with mean 1/2. What happens at the first vertex is governed by m+, and at the second by m-. For each vertex P, we construct a sequence of stopping times along which the image of the whole circle by K is reduced to P. We also prove that the supports of these flows contains a finite number of points, and that except for some particular cases this number of points can be arbitrarily large.