Titlebook: Stochastic Neutron Transport; And Non-Local Branch Emma Horton,Andreas E. Kyprianou Book 2023 The Editor(s) (if applicable) and The Author(

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Classical Neutron Transport Theorymily of radiation transport equations, all of which are variants of a general category of Boltzmann transport equations. Our objective in this book is to assemble some of the main mathematical ideas around neutron transport and their relationship with the modern theory of branching Markov processes.

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Some Background Markov Process Theoryepeatedly in our calculations. After a brief reminder of some basics around the Markov property, we will focus our attention on what we will call expectation semigroups. These are the tools that we will use to identify neutron density and provide an alternative representation of solutions to the NTE

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Many-to-One, Perron–Frobenius and Criticalityl in this respect is to understand how to provide a rigorous analogue of the spectral asymptotic behaviour given in Theorem . for the NTE as an . solution but now for the setting of . solutions that emerge from our mild NTE formulation (.). The way we will do this is to draw the general Perron–Frobe

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Pál–Bell Equation and Moment Growth we can glean about the NBP from the NTE. Recall that the NBP is fundamentally our physical model of fission in an inhomogeneous material and so many questions will go beyond what linear equations can tell us. In this respect, our starting point is the Pál–Bell equation, a non-linear equation which