  A correlated Gaussian random walk(CGRW) model is proposed as a simple model
of animal dispersal. The general features of CGRW is described. We will discuss
how from this single model a number of different kinds of correlated random
walk can be studied. The CGRWs in one dimension is studied in detail and the
special limiting cases are discussed where the probability densities are found
analytically. Numerical simulations are performed and the results are found to
be in good agreement with the theoretical predictions. Directional persistence
in CGRWs is discussed for the one dimensional cases. We will show that
correlation does not always give rise to directional persistence.
