  In this work we study stochastic Oldroyd type models for viscoelastic fluids
in $\mathbb{R}^d, d= 2, 3$. We show existence and uniqueness of strong local
maximal solutions when the initial data are in $H^s$ for $s>d/2, d= 2, 3$.
Probabilistic estimate of the random time interval for the existence of a local
solution is expressed in terms of expected values of the initial data.
