Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean m agnetization" for a family of Gaussian Markov processes indexed by a positi ve parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increas es, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the mome nts of the distribution for arbitrary alpha. For some special values of alp ha, we obtain closed form expressions of the distribution function. [S1063- 651X(99)03306-1].