Some remarks on minimax sequential tests for stationary ornstein–uhilenbeck processes

Abstract

In this paper sequential tests of one sided hypotheses H₁ : μ ≤ μ₀ and H₂ : μ > μ₀ for the velocity parameter of a stationary Ornstein-Uhlenbeck process(OUP) are discussed. When the variance parameter of the OUP is known the results obtained here complement a recent work of Roters (1991) by proving the existence of minimax sequential tests under concave and symmetric (about μ₀) loss l(μ)with l(μ₀) > 0 and linear costs of observation. For unkown variance parameter minimax sequential tests are derived for all loss functions discussed here and in the above mentioned paper.

Keywords:

• stationary Ornstein-Uhlenbeck process
• minimax sequential test
• ∊-minimax sequential test
• symmetric Wald SPRT