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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 10, Fasc. 1,
pages 27 - 44
 

FIRST HITTING TIMES AND POSITIONS OF CONCENTRIC SPHERES FOR TESTING THE DRIFT OF A DIFFUSION PROCESS

V. Genon-Catalot

Abstract: Consider X
  t  a diffusion process on Rm, m > 2, with drift vector hb(u) depending of an unknown real parameter h with small known variance matrix es(u). The aim of this paper is testing h = h
    0  vs h > h
    0  with h > 0
 0 from the observation of the first hitting times and positions of concentric spheres centered at x = X
     0  with radii r < R for given R. We obtain the asymptotic behaviour of this process as e-- > 0 when the trajectory of the corresponding dynamical system leaves any sphere centered at x within finite time. We then construct a test on h and study its asymptotic properties by means of contiguity. When h  > 0,
 0 the test is locally asymptotically most powerful (LAMP). We also consider a test based on the first hitting times of spheres only.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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