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Switching Diffusion Systems With Past-Dependent Switching Having A Countable State Space, Hai Dang Nguyen
Switching Diffusion Systems With Past-Dependent Switching Having A Countable State Space, Hai Dang Nguyen
Wayne State University Dissertations
Emerging and existing applications in wireless communications, queueing networks, biological models, financial engineering, and social networks demand the
mathematical modeling and analysis of hybrid models in which continuous dynamics and discrete events coexist.
Assuming that the systems are in continuous times,
stemming from stochastic-differential-equation-based models and random discrete events,
switching diffusions come into being. In such systems, continuous states and discrete events
(discrete states)
coexist and interact.
A switching diffusion is a two-component process $(X(t),\alpha(t))$, a continuous component and a discrete component taking values in a discrete set (a set consisting of isolated points).
When the discrete component takes a …