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Time Reversal for Gap Diffusions with Nonlocal Boundary Conditions

Matthias Weber

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Abstract

Abstract We consider the infinitesimal generator of the time reversal of a time‐homogeneous one‐dimensional gap diffusion with state space [0, 1] given by the infinitesimal generator Ao = dDs+ ‐ dk / dm with nonlocal boundary conditions of Feller‐Wentzell‐type. This leads to an infinitesimal generator which belongs to a class of generators introduced in the earlier note [W1].

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Abstract We consider the infinitesimal generator of the time reversal of a time‐homogeneous one‐dimensional gap diffusion with state space [0, 1] given by the infinitesimal generator Ao = dDs+ ‐ dk / dm with nonlocal boundary conditions of Feller‐Wentzell‐type. This leads to an infinitesimal generator which belongs to a class of generators introduced in the earlier note [W1].

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Available abstract

Abstract We consider the infinitesimal generator of the time reversal of a time‐homogeneous one‐dimensional gap diffusion with state space [0, 1] given by the infinitesimal generator Ao = dDs+ ‐ dk / dm with nonlocal boundary conditions of Feller‐Wentzell‐type. This leads to an infinitesimal generator which belongs to a class of generators introduced in the earlier note [W1].

Key concepts: Infinitesimal, Mathematics, Generator (circuit theory), Boundary (topology), Homogeneous, Mathematical analysis, Type (biology), Infinitesimal transformation

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