大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Asymptotically distribution free test for diffusion by different sample schemes

Ilia Negri (Department of Information Technology and Mathematical Methods, University of Bergamo (Italy))

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大阪大学 金融・保険セミナーシリーズ 第19回

Asymptotically distribution free test for diffusion by different sample schemes

Ilia Negri (Department of Information Technology and Mathematical Methods, University of Bergamo (Italy))

We consider nonparametric goodness of fit test problem for
the drift coefficient of a one-dimensional ergodic diffusions.
We present results based on three different sample scheme: continuous
time observation, discrete time observation and tick time sample.
We study the limit distribution of the proposed test statistics
based on different sample schemes and we prove that it is the
supremum of the standard Brownian motion in the three considered cases.
We also show that the tests are consistent under any fixed alternatives.