This monograph highlights the connection between the theory of neutron transport and the theory of non-local branching processes. By detailing this frequently overlooked relationship, the authors provide readers an entry point into several active areas, particularly applications related to general radiation transport. Cutting-edge research published in recent years is collected here for convenient reference. Organized into two parts, the first offers a modern perspective on the relationship between the neutron branching process (NBP) and the neutron transport equation (NTE), as well as some of the core results concerning the growth and spread of mass of the NBP. The second part generalizes some of the theory put forward in the first, offering proofs in a broader context in order to show why NBPs are as malleable as they appear to be. Stochastic Neutron Transport will be a valuable resource for probabilists, and may also be of interest to numerical analysts and engineers in the field of nuclear research.
Part I Neutron Transport Theory.- Classical Neutron Transport Theory.- Some background Markov process theory.- Stochastic Representation of the Neutron Transport Equation.- Many-to-one, Perron-Frobenius and criticality.- Pal-Bell equation and moment growth.- Martingales and path decompositions.- Discrete evolution.- Part II General branching Markov processes.- A general family of branching Markov processes.- Moments.- Survival at criticality.- Spines and skeletons.- Martingale convergence and laws of large numbers.
Emma Horton completed her PhD in 2019 at the University of Bath, where she also completed her undergraduate and masters studies. Following her PhD, she became a postdoc at the IECL, Université de Lorraine. Thereafter, she became chargée de recherche with the project-team ASTRAL, INRIA. She spent over six months as a visiting researcher to the University of Melbourne in 2023 and is currently an Assistant Professor at the University of Warwick, Department of Statistics.
Andreas E. Kyprianou was educated at the University of Oxford and University of Sheffield and is currently a professor of probability theory at the University of Warwick. He has spent almost 30 years working on the theory and application of path-discontinuous stochastic processes and has over 130 publications, including three graduate textbooks. Before moving to Warwick, Andreas spent a large portion of his career at the University of Bath, Department of Mathematical Sciences. Prior to that, he heldvarious positions at the University of Edinburgh, Heriot Watt University, The London School of Economics, as well as working for nearly two years in the oil industry.
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