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

We 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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Houston

Year dc:date.issued

2020

Author dc:creator

• Chen, Xi

Advisor dc:contributor.advisor

• Timofeyev, Ilya

Committee members dc:contributor.committeemember

• Török, Andrew
• Ott, William
• Abramov, Rafail V.

• stochastic differential equations
• drift and diffusion estimation
• conditional expecta- tion
• mean squared error
• regression

Statement dc:rights

• The 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).

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/10657/7018

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/7018