This paper addresses the control of spatially distributed processes. We utilize a distributed architecture in which multiple local controllers coordinate their efforts through a data network that allows information exchange. We focus our work on linear time invariant processes disturbed by Gaussian white noise and propose several logics to determine when the local controllers should communicate. We provide conditions under which these logics guarantee boundedness and investigate the trade-off between the amount of information exchanged and the performance achieved. The resulting closed-loop systems evolve according to stochastic differential equations with resets triggered by stochastic counters. This type of stochastic hybrid system seems to be interesting on its own. The theoretical results are validated through Monte Carlo simulations.