Jump processes on leaves of multibranching trees - Mathematical PhysicsReport as inadecuate




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Abstract: The p-adic numbers have found applications in a wide range of diverse fieldsof research. In some applications the algebraic properties of p-adics enter asan indispensable ingredient of the theory. Another class of applications has todo with hierarchical tree like systems. In this context the applications arebased on the well known correspondence between p-adics and the trees withp-branches emerging from every branching point. Then the algebraic structuredoes not enter and p-adics are used merely as a labeling system for the treebranches. We introduce a space of numerical sequences suitable for labeling thetrees with varying number of branches emerging from the branching points. Weequipe this space with a non Archimedian metric and describe its basictopological properties. We also demonstrate that the known construction of thestochastic processes on p-adics carry over to the stochastic processes on theabove mentioned space and hence on the corresponding trees.



Author: Sergio Albeverio, Witold Karwowski

Source: https://arxiv.org/







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