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arXiv · 2111.14601

Elastic drifted Brownian motions and non-local boundary conditions

Mirko D'Ovidio·Francesco Iafrate
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Abstract

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 multiplicative functional associated with fractional boundary conditions of tempered type. By exploiting such connection we write some functionals in terms of a simple (positive and non-decreasing) process. In our view, such a representation is useful in many applications.

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Mirko D'Ovidio, Francesco Iafrate. 2021-11-29. Elastic drifted Brownian motions and non-local boundary conditions. https://arxiv.org/abs/2111.14601

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