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Stochastic differential equations have been used intensively in stochastic control. In this paper, we present 2-dimensional Poisson Counter Driven Stochastic Differential Equation (PCSDE) models that lead to correlated bivariated power law behaviors. We propose two types of 2D PCSDE models and study their tail dependence behavior. The first model generates tail dependence coefficient with values either...
In this paper we present simple stochastic differential equations that lead to lower-tail and/or upper tail power law behaviors. We also present a model with bi-directional Poisson counters that exhibits power law behavior near a critical point, which might be of interest to statistical physics.
Queuing analysis is important in providing guiding principles for packet network analysis. Stochastic fluid queueing models have been widely used as burst scale models for high speed communication networks. In this paper, we propose a novel two-level Markov on-off source model to model the burstiness of a packet stream at different time scales. Analytical results are obtained to reveal the impact...
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