Continuous dependence and time change for Ito equations
The paper concerns continuous dependence on the drift term and the invariants for Ito equations when a time change is performed. The continuity property with respect to drift terms is proved using a weaker topology than usually required and the distance between solutions is measured by the usual metric. For deterministic autonomous differential equations the invariant under a time change is the trajectory: in the case of Ito equations it is shown that such invariant is the set \(\overline{\cup_{t\leq 0}\sup p} P_ t(.)\), where \(P_ t(.)\) is the probability measure generated on \(R^ n\) by the random vector x(t,.). By an appropriate time change an Ito equation with unbounded coefficients can be transformed into one with bounded coefficients and this change gives an alternative way for extending to the case of unbounded coefficients the description of the above set as the attainable set of a deterministic control system.
continuity property with respect to drift terms
scientific article; zbMATH DE number 3850203
scientific article