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Elastic drifted Brownian motions and non-local boundary conditions

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DOI: 10.1016/j.spa.2023.104228

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This article explores the connection between elastic drifted Brownian motions and inverses to tempered subordinators, and establishes a link between multiplicative functionals and dynamical boundary conditions. By representing functionals of the drifted Brownian motion as the inverse of a tempered subordinator, the problem is simplified.
We provide a deep connection between elastic drifted Brownian motions and inverses to tempered subordinators. Based on this connection, we establish a link between multiplicative functionals and dynamical boundary conditions given in terms of non-local equations in time. Indeed, we show that the multiplicative functional associated to the elastic Brownian motion with drift is equivalent to a functional associated with non-local boundary conditions of tempered type. By exploiting such connections we write some functionals of the drifted Brownian motion in terms of a simple (positive and non-decreasing) process, the inverse of a tempered subordinator. In our view, such a representation is useful in many applications and brings new light on dynamic boundary value problems.(c) 2023 Elsevier B.V. All rights reserved.

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