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Titlebook: Stochastic and Infinite Dimensional Analysis; Christopher C. Bernido,Maria Victoria Carpio-Berni Conference proceedings 2016 Springer Inte

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Principal Solutions Revisited,uced by Leighton and Morse in the scalar context in 1936 and by Hartman in the matrix-valued situation in 1957, with Weyl–Titchmarsh solutions, as long as the underlying Sturm–Liouville differential expression is nonoscillatory (resp., disconjugate or bounded from below near an endpoint) and in the
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Stochastic Processes on Ends of Tree and Dirichlet Forms,s. In one of them the trees are represented by spaces of numerical sequences and the processes are obtained by solving a class of Chapman-Kolmogorov Equations. In the other the trees are described by the set of nodes and edges. To each node there is naturally associated a finite dimensional function
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,Stochastic Solutions of Nonlinear PDE’s and an Extension of Superprocesses,ion. There are two different approaches for the construction of stochastic solutions: MacKean’s and superprocesses. Here one shows how to extend the McKean construction to equations with derivatives and non-polynomial interactions. On the other hand, when restricted to measures, superprocesses can o
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Principal Solutions Revisited,g as the underlying Sturm–Liouville differential expression is nonoscillatory (resp., disconjugate or bounded from below near an endpoint) and in the limit point case at the endpoint in question. In addition, we derive an explicit formula for Weyl–Titchmarsh functions in this case (the latter appears to be new in the matrix-valued context).
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