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Full-Text Articles in Physical Sciences and Mathematics
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 …
Hardy Space Theory And Endpoint Estimates For Multi-Parameter Singular Radon Transforms, Jiawei Shen
Hardy Space Theory And Endpoint Estimates For Multi-Parameter Singular Radon Transforms, Jiawei Shen
Wayne State University Dissertations
In [12], Christ, Nagel, Stein and Waigner studied the L p theories for the singular Radon Trans-
forms. Furthermore, B. Street in [68], and Stein and Street in [64–67] extended the theories of the
L p boundedness for multi-parameter singular integral operators, such as the Calderón Zygmund
operators and singular Radon transforms. In this dissertation, we will study the Hardy space H p
and its dual space associated with both the one-parameter and multi-parameter singular Radon
transforms, and consider the boundedness of the singular Radon transforms on such Hardy spaces
H p when 0 ≤ p ≤ 1.
Inspired by …