0000000000025276
AUTHOR
Witold Karwowski
showing 2 related works from this author
Stochastic Processes on Ends of Tree and Dirichlet Forms
2016
We present main ideas and compare two constructions of stochastic processes on the ends (leaves) of the trees with varying numbers of edges at the nods. 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 space and the Dirichlet form on it. Having a class of Dirichlet forms at the nodes one can under certain conditions build a Dirichlet form on L2 space of funcions on the ends of the trees. We show that the state spaces of two approaches are homeomo…
Generators of Random Processes in Ultrametric Spaces and Their Spectra
2009
The L 2(\( \mathbb{S} \)) space of square integrable functions on an ultrametric space \( \mathbb{S} \) has rather specific structure. As a consequence in a natural way there appear in L 2(\( \mathbb{S} \)) the operators of which unitary counterparts in L 2(ℝn) would be difficult to construct. Such class of self-adjoint operators emerge from theory of random processes on ultrametric spaces. In this paper we collect known material on spectral properties of the generators of random processes on \( \mathbb{S}_B \) an ultrametric space of sequences. (The set of p-adic numbers is a subset of \( \mathbb{S}_B \).) Then we discuss structure of the eigenspaces of the generators.