Concatenation of nonhonest Feller processes, exit laws, and limit theorems on graphs. (English) Zbl 1528.60043
Summary: We provide a rather explicit formula for the resolvent of a concatenation of \(N\) processes in terms of their exit laws and certain probability measures characterizing the way the processes are concatenated. As an application, we prove an averaging principle saying that by concatenating asymptotically splittable processes one can approximate Markov chains.
MSC:
| 60G53 | Feller processes |
| 35B25 | Singular perturbations in context of PDEs |
| 35F46 | Initial-boundary value problems for systems of linear first-order PDEs |
| 35K57 | Reaction-diffusion equations |
| 60J35 | Transition functions, generators and resolvents |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 47D07 | Markov semigroups and applications to diffusion processes |
Keywords:
exit laws; processes on metric graphs; concatenation of processes; nonlocal boundary and transmission conditions; Feller processes; snapping out and skew Brownian motionsSoftware:
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