機率研討會
主講者: 傅權教授 (University of Manitoba)
講題: Finite Markov Chain Imbedding Approximation
時間: 2012-12-03 (Mon.)  14:10 -
地點: 數學所 617 研討室 (台大院區)
Abstract: Let $X_{n}\left ( \wedge \right )$ be the number of non-overlapping occurrences of a simple pattern $\wedge $ in a sequence of independent and identically distributed [i.i.d.] multi-state trials. For fixed $k$, the exact tail probability $\mathbb{P}\left \{ X_{n}\left ( \wedge \right )< k \right \}$ is diffcult to compute and tends to 0 exponentially as $n \to \infty $. In this paper, we use the finite Markov chain imbedding technique and standard matrix theory results to obtain an approximation for this tail probability. The result is extended to compound patterns, Markov dependent multi-state trials and overlapping occurrences of $\wedge $. Numerical comparisons with the normal approximation are provided. Results indicate that the proposed approximations perform very well and do significantly better than the normal approximation in many cases.
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