摘要：We study the dynamics of the family of copulas { C t } t ≥0 of a pair of stochastic processes given by stochastic differential equations (SDE). We associate to it a parabolic partial differential equation (PDE). Having embedded the set of bivariate copulas in a dual of a Sobolev Hilbert space H 1 (ℝ 2 ) * we calculate the derivative with respect to t and the *weak topology i.e. the tangent vector field to the image of the curve t → C t . Furthermore we show that the family { C t } t ≥0 is an orbit of a strongly continuous semigroup of transformations and provide the infinitesimal generator of this semigroup..
