Brownian Bridge and Other Path-dependent Gaussian Processes Vectorial Simulation |
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| Authors: | J Beleza Sousa M L Esquível R M Gaspar |
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| Institution: | 1. M2A/ADEETC, Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, Lisboa, Portugal;2. CMA/DM, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugaljsousa@deetc.isel.ipl.pt;4. CMA/DM, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal;5. CEMAPRE, ISEG, Universidade de Lisboa, Lisboa, Portugal |
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| Abstract: | The iterative simulation of the Brownian bridge is well known. In this article, we present a vectorial simulation alternative based on Gaussian processes for machine learning regression that is suitable for interpreted programming languages implementations. We extend the vectorial simulation of path-dependent trajectories to other Gaussian processes, namely, sequences of Brownian bridges, geometric Brownian motion, fractional Brownian motion, and Ornstein–Ulenbeck mean reversion process. |
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| Keywords: | Brownian bridge Gaussian processes for machine learning regression Path-dependent Gaussian processes Vectorial simulation |
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