Uniform concentration inequality for ergodic diffusion processes observed at discrete times

2011/09/15 by Leonid Galtchouk, Serguei Pergamenchtchikov, Galtchouk, Leonid +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1109.3406

arxiv created 2011/09/15 · arxiv updated 2011/09/16

Abstract

In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes. As an application we consider the nonparametric pointwise estimation problem for the drift coefficient under discrete time observations.

Related

• Concentration of scalar ergodic diffusions and some statistical\n implications
• Geometric ergodicity for families of homogeneous Markov chains
• A note on the uniform ergodicity of diffusion processes
• Concentration inequality for U-statistics of order two for uniformly ergodic Markov chains
• Evolution of Gaussian Concentration Bounds under Diffusions