Constrained Stochastic Differential Equations Driven by Fractional Brownian Motions: Stationarity and Parameter Estimation Problems
Final rept. 1- Sep 2012-9 Jun 2013
COLORADO STATE UNIV FORT COLLINS OFFICE OF SPONSORED RESEARCH
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We study stationary solutions of constrained stochastic differential equations driven by fractional Brownian motions. Key motivations for this study originate from the fact that such constrained processes serve as approximation models for a large class of stochastic networks in heavy traffic with long range dependence and self similarity characteristics of data traffic, which are empirically observed in several kinds of local area networks and internet systems. The key mathematical result is a tightness in time of the constrained stochastic processes. In a framework of Stochastic Dynamical Systems i.e. infinite dimensional state space setting that pertains to noise process with memory, such a tightness result essentially establishes the existence of the stationary solutions. We also address a family of parameter estimation problems for stochastic processes driven by fractional Brownian motions. Parameter estimation problems are usually quite difficult in the physical network models with or without long memory, whereas the limit stochastic differential models can be much more tractable for statistical analysis.
- Physical Chemistry
- Theoretical Mathematics
- Statistics and Probability