RT Journal Article
T1 Nonparametric estimation of stochastic differential equations with sparse Gaussian processes
A1 García Martínez, Constantino Antonio
A1 Otero, Abraham
A1 Félix Lamas, Paulo
A1 Rodríguez Presedo, Jesús María
A1 Márquez, David G.
AB The application of stochastic differential equations (SDEs) to the analysis of temporal data has attractedincreasing attention, due to their ability to describe complex dynamics with physically interpretable equations.In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs froma densely observed discrete time series. The use of Gaussian processes as priors permits working directly in afunction-space view and thus the inference takes place directly in this space. To cope with the computationalcomplexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided.This approximation permits the efficient computation of predictions for the drift and diffusion terms by using adistribution over a small subset of pseudosamples. The proposed method has been validated using both simulateddata and real data from economy and paleoclimatology. The application of the method to real data demonstratesits ability to capture the behavior of complex systems
PB APS Physics
SN 2470-0045
YR 2017
FD 2017
LK http://hdl.handle.net/10347/17720
UL http://hdl.handle.net/10347/17720
LA eng
NO García, C., Otero, A., Félix, P., Presedo, J., & Márquez, D. (2017). Nonparametric estimation of stochastic differential equations with sparse Gaussian processes. Physical Review E, 96(2). doi: 10.1103/physreve.96.022104
NO This work has received financial support from the Consellería de Cultura, Educación e Ordenación Universitaria da Xunta de Galicia and the European Regional DevelopmentFund (ERDF) under Grant No. 2016-2019-ED431G/08, by the Spanish MINECO under Project No. TIN2014-55183-R, and by the Universidad San Pablo CEU under Grant No.PCON10/2016. C.A.G. acknowledges the support of the FPU fellowship from the Spanish MECD with Ref. No. FPU14/02489
DS Minerva
RD 27 abr 2026