B0762
Title: On copulas of a Wiener process and its running maxima and running minima processes
Authors: Piotr Jaworski - University of Warsaw (Poland) [presenting]
Abstract: A three-variate copula of a triple of self-similar stochastic processes: a Wiener process $W_t$, $t\ge 0$, its running maxima process $M_t=\sup \{W_s: 0\le s \le 1\}$ and its running minima process $m_t=\inf \{W_s: 0\le s\le 1\}$ and its bivariate margins are the objectives. The analytical formulas for these copulas and their densities are derived, and their supports are characterized. For marginals, the Spearman $\rho$ is calculated.
