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arXiv · 1704.07644

Constraint Ornstein-Uhlenbeck bridges

Alain Mazzolo
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Abstract

In this paper, we study the Ornstein-Uhlenbeck bridge process (i.e. the Ornstein-Uhlenbeck process conditioned to start and end at fixed points) constraints to have a fixed area under its path. We present both anticipative (in this case, we need the knowledge of the future of the path) and non-anticipative versions of the stochastic process. We obtain the anticipative description thanks to the theory of generalized Gaussian bridges while the non-anticipative representation comes from the theory of stochastic control. For this last representation, a stochastic differential equation is derived which leads to an effective Langevin equation. Finally, we extend our theoretical findings to linear bridge processes.

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Alain Mazzolo. 2017-04-25. Constraint Ornstein-Uhlenbeck bridges. https://doi.org/10.1063/1.5000077

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