In this talk, we present some recent applications of Shrinkage and Pretest strategies in some multiple multivariate stochastic processes. More precisely, we consider the estimation problem for the drift parameters matrices of M independent multivariate diffusion processes. In particular, we study the problem where the M-parameters matrices may satisfy uncertain constraints. In order to account for both the sample information and uncertain prior non-sample information, we develop a class of estimators which encloses as special cases the maximum likelihood estimator (MLEs) and shrinkage estimators (SEs). In particular, the established SEs showcase the well known Stein’s phenomenon. Also, we extend some recent asymptotic results in Kutoyants (2004) as well as that in Nkurunziza and Ahmed (2010). Further, in order to derive the asymptotic distributional risk and bias of the established class of estimators, we extend some classical identities.