Brownian Bridge and Other Path-dependent Gaussian Processes Vectorial Simulation

Jorge A. M. Sousa; M. L. Esquível; R. M. Gaspar

doi:10.1080/03610918.2014.901352

Brownian Bridge and Other Path-dependent Gaussian Processes Vectorial Simulation

Jorge A. M. Sousa, M. L. Esquível, R. M. Gaspar

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2608-2621
Number of pages	14
Journal	Communications in Statistics: Simulation and Computation
Volume	44
Issue number	10
DOIs	https://doi.org/10.1080/03610918.2014.901352
Publication status	Published - Nov 2015

Keywords

Brownian bridge
Gaussian processes for machine learning regression
Path-dependent Gaussian processes
Vectorial simulation

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10.1080/03610918.2014.901352

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title = "Brownian Bridge and Other Path-dependent Gaussian Processes Vectorial Simulation",

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.",

keywords = "Brownian bridge, Gaussian processes for machine learning regression, Path-dependent Gaussian processes, Vectorial simulation",

author = "Sousa, {Jorge A. M.} and Esqu{\'i}vel, {M. L.} and Gaspar, {R. M.}",

note = "J. Beleza Sousa was partially supported by the ISEL/IPL scholarship SFRH/PROTEC/49576/2009. R. M. Gaspar's research was partially supported by the SANAF project, financed by the Portuguese Science Foundation with project reference number UTA CMU/MAT/0006/2009.",

year = "2015",

month = nov,

doi = "10.1080/03610918.2014.901352",

language = "English",

volume = "44",

pages = "2608--2621",

journal = "Communications in Statistics: Simulation and Computation",

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TY - JOUR

T1 - Brownian Bridge and Other Path-dependent Gaussian Processes Vectorial Simulation

AU - Sousa, Jorge A. M.

AU - Esquível, M. L.

AU - Gaspar, R. M.

N1 - J. Beleza Sousa was partially supported by the ISEL/IPL scholarship SFRH/PROTEC/49576/2009. R. M. Gaspar's research was partially supported by the SANAF project, financed by the Portuguese Science Foundation with project reference number UTA CMU/MAT/0006/2009.

PY - 2015/11

Y1 - 2015/11

N2 - 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.

AB - 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.

KW - Brownian bridge

KW - Gaussian processes for machine learning regression

KW - Path-dependent Gaussian processes

KW - Vectorial simulation

UR - http://www.scopus.com/inward/record.url?scp=84937435807&partnerID=8YFLogxK

U2 - 10.1080/03610918.2014.901352

DO - 10.1080/03610918.2014.901352

M3 - Article

AN - SCOPUS:84937435807

SN - 0361-0918

VL - 44

SP - 2608

EP - 2621

JO - Communications in Statistics: Simulation and Computation

JF - Communications in Statistics: Simulation and Computation

IS - 10

ER -

Brownian Bridge and Other Path-dependent Gaussian Processes Vectorial Simulation

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Keywords

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