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A probabilistic approach to a non‐local quadratic form and its connection to the Neumann boundary condition problem
Author(s) -
Vondraček Zoran
Publication year - 2021
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900061
Subject(s) - mathematics , probabilistic logic , connection (principal bundle) , neumann boundary condition , quadratic equation , dirichlet distribution , operator (biology) , von neumann architecture , interpretation (philosophy) , affiliated operator , von neumann's theorem , boundary (topology) , pure mathematics , boundary value problem , mathematical analysis , computer science , geometry , statistics , multiplication operator , biochemistry , chemistry , repressor , hilbert space , transcription factor , programming language , gene
In this paper we look at a probabilistic approach to a non‐local quadratic form that has lately attracted some interest. This form is related to a recently introduced non‐local normal derivative. The goal is to construct two Markov processes: one corresponding to that form and the other which is related to a probabilistic interpretation of the Neumann problem. We also study the Dirichlet‐to‐Neumann operator for non‐local operators.