Consistency and Convergence of Non-parametric Estimation of Drift and Diffusion Coefficients in SDEs from Long Stationary Time-series

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dc.contributor.advisorTimofeyev, Ilya
dc.contributor.committeeMemberTörök, Andrew
dc.contributor.committeeMemberOtt, William
dc.contributor.committeeMemberAbramov, Rafail V.
dc.creatorChen, Xi
dc.date.accessioned2020-10-09T20:30:20Z
dc.date.available2020-10-09T20:30:20Z
dc.date.createdAugust 2020
dc.date.issued2020-08
dc.date.submittedAugust 2020
dc.date.updated2020-10-09T20:30:24Z
dc.description.abstractWe study the efficiency of non-parametric estimation of stochastic differential equations driven by Brownian motion (i.e. diffusions) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is motivated by the definition of drift and diffusion coefficients for SDEs. These estimators involve time- and space-discretization parameters for computing discrete analogs of expected values from discretely-sampled stationary data. Number of observational points is the third important computational parameter. Next, we derive bounds for the asymptotic behavior of L2 errors for the drift and diffusion estimators. The asymptotic behavior is characterized when the number of observational points becomes infinite and observational time-step and bin size for spatial discretization of drift and diffusion coefficients tend to zero. Using our asymptotic analysis we are able to obtain practical guidelines for selecting computational parameters. Finally, we perform a series of numerical simulations which support our analytical investigation and illustrate practical guidelines for selecting near-optimal and computationally efficient values for computational parameters.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10657/7018
dc.language.isoeng
dc.rightsThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).
dc.subjectstochastic differential equations
dc.subjectdrift and diffusion estimation
dc.subjectconditional expecta- tion
dc.subjectmean squared error
dc.subjectregression
dc.titleConsistency and Convergence of Non-parametric Estimation of Drift and Diffusion Coefficients in SDEs from Long Stationary Time-series
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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