Stochastic Approximation with Asymptotic Martingale Perturbations
碩士 === 國立彰化師範大學 === 統計資訊研究所 === 95 === This thesis consists of two parts. In Chapter 1, we generalize some results of Lai and Robbins (1979) to include stochastic approximations with asymptotic martingale perturbations under some moment condition instead of i.i.d. noises. The simulation study veri...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2007
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| Online Access: | http://ndltd.ncl.edu.tw/handle/37761946710034824177 |
| Summary: | 碩士 === 國立彰化師範大學 === 統計資訊研究所 === 95 === This thesis consists of two parts. In Chapter 1, we generalize some results of Lai and Robbins (1979) to
include stochastic approximations with asymptotic martingale perturbations under some moment condition instead of i.i.d. noises.
The simulation study verifies the validity of our results of convergence of iterations. In Chapter 2, We focus on another paper by Lai and Robbins (1979b) and try to study the rate of convergence of stochastic approximation when the perturbation is relaxed to comprise a martingale sequence by utilizing a Marcinkiewcz-Zygmund type law of large numbers for martingale. Finally, we also provide an illustrative simulation.
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