Stochastic processing networks with coupled transition rates
Modern resource sharing mechanisms for data networks, such as peer-to-peer file distribution protocols, can often be modeled as stochastic processing networks where the input and output rates at a node depend on the state of all other nodes in the network. When the transition rates are coupled this way, traditional techniques of queueing theory are not generally applicable. Hence there is a demand for new stability analysis and performance evaluation tools based on stochastic monotonicity, coupling, and martingales.
Self-similar random fields with long-range dependence
Fractional Gaussian noise is a natural model for long-range dependent spatial random phenomena. Because its use involves some knowledge of generalized functions, it has not yet been widely popular in applied sciences. An interesting theoretical problem is look whether various better known spatial models, such as the Lévy's fractional Brownian field and the fractional Brownian sheet, have simple integral representations with respect to fractional Gaussian noise.
Comparison of partially observed stochastic processes
When continous-time random processes are observed sequentially in discrete time intervals, the resulting times series represents an incomplete description of the underlying process. An interesting question is to find upper and lower bounds for functionals of the underlying process, conditional on the observed time series. Applications of this type of monotonicity results include prediction of packet loss in data networks and estimation of financial risk.