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No-flux boundary conditions for one-sided Lévy processes

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FD2W01 - Deterministic and stochastic fractional differential equations and jump processes

We connect the generators of one-sided L\’evy processes restricted to the interval [0,1] with boundary conditions for one-sided pseudo-differential operators, generalising results for Caputo derivatives of order in (1, 2). We consider killing (Dirichlet), reflecting (Neumann) and fast-forwarding (non-local Neumann) boundary conditions. To identify the backward and forward equations for these Feller processes, we develop a Gr\”unwald-type (random walk) approximation on [0,1]. In particular, this shows rigorously and intuitively howthe non-local Neumann boundary condition arises from mass conservation. Joint work with Boris Baeumer (University of Otago) and Mih\’alyKov\’acs (P\’azm ́any P\’eter Catholic University).

This talk is part of the Isaac Newton Institute Seminar Series series.

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