Phys.[**[7]{}**]{}, 91 (1983).

G. Paladin and S. Vaienti, J. Math. Phys. A[**[21]{}**]{}, 4609 (1988).

F.Y. Hunt and W.M. Miller, J. Stat. Phys.[**[66]{}**]{}, 535 (1992).

E. Ott, [*Chaos in Dynamical Systems*]{}, Cambridge University Press, Cambridge (1993).

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller and E. Teller, J. Chem. Phys.[**[21]{}**]{}, 1087 (1953).

D. Pingel, P. Schmelcher and F. K. Diakonos, Phys. Rev.E [**[58]{}**]{}, 369 (1998).

H. Mori, B. So and T. Ose, Progr. of Theor.Phys.[**[66]{}**]{}, 1266 (1981).

S. Grossmann and H. Horner, Z. Phys. B [**60**]{}, 79 (1985).

[[**[FIGURE CAPTIONS]{}**]{}]{}

[**Figure 1:**]{} The stochastic minimization results for a dynamical system with uniform invariant density and exponentially decaying autocorrelation function. (a) The resulting map using model I. (b) The autocorrelation function for the map of model I (solid line) and the corresponding prescribed data (full circles). (c) The resulting map using model II. (d) The autocorrelation function for the map of model II (solid line) and the corresponding prescribed data (full circles).

[**Figure 2:**]{} Same as in figure 1 but for prescribed linear invariant density and exponentially decaying autocorrelation function.

[**Figure 3:**]{} Same as in figure 1 but for prescribed power-law invariant density ($\beta=-0.5$) and oscillatory decaying autocorrelation function.

[**Figure 4:**]{} Same 