Branching one-dimensional periodic diffusion processes |
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Authors: | Nobuyuki Ikeda Kiyoshi Kawazu Yukio Ogura |
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Institution: | Department of Mathematics, Osaka University, Toyonaka, Osaka 560, Japan;Department of Mathematics, Faculty of Education, Yamaguchi University, Yamaguchi 753, Japan;Department of Mathematics, Saga University, Saga 840, Japan |
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Abstract: | Let X be a nonsingular conservative one-dimensional periodic diffusion process, λ0 its principal eigenvalue and X a binary splitting branching diffusion process with nonbranching part X. For each α > λ0 we have two positive martingales Wit(α), i = 1, 2, of X attached to the two positive α-harmonic functions of X. The main purpose of this paper is to show that their limit random variables are positive for all α? (λ0, αi), where αi are some constants greater than λ0. |
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Keywords: | periodic diffusion process Hill's equations principal eigenvalue λ-harmonic function branching process limit theorem |
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