%0 Journal Article %T Residence Time Distribution for a Class of Gaussian Markov Processes %A Abhishek Dhar %A Satya N. Majumdar %J Physics %D 1999 %I arXiv %R 10.1103/PhysRevE.59.6413 %X We study the distribution of residence time or equivalently that of ``mean magnetization" for a family of Gaussian Markov processes indexed by a positive 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 $\theta$ increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary $\alpha$. For some special values of $\alpha$, we obtain closed form expressions of the distribution function. %U http://arxiv.org/abs/cond-mat/9902004v3