| Budget Amount *help |
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Research Abstract |
Monte Carlo method can be widely applied to various types of problems. Therefore, we can apply the method to problems that is hard to solve based on analytical methods. When these analytically difficult problems are solved using the Monte Carlo method, its efficient method is indispensable. So, this study tried to develop the efficient methods, which contain a method depends on precision of pseudorandom numbers
This study classified a Monte Carlo method into two types. One type is a Monte Carlo method that is used in integral problems. Another one is a method in which the relevant phenomena are simulated. It should be noted that the term of the hit-or-miss Monte Carlo method is not used only in the integral problems but also in the phenomena simulation problems. Because we can take many advantages of efficient methods in case of the integral problem, this study proposed such classification.
At the first half of this study, the phenomena simulation type of Monte Carlo method was considered and its efficient method was developed. Generally, the Monte Carlo calculation problems can be expressed in integral forms. However, some problems need adequate consideration in expression of integral. In such cases, the phenomena simulation type of Monte Carlo method can be conveniently applied.
The latter half of this study considered uniformly distributed pseudorandom numbers that emphasize its probabilistic uniformity. This is based on an idea that is used in quasi-Monte Carlo method. Through several numerical examples, it was shown that efficient Monte Carlo computation be realized, when the proposed pseudorandom numbers were used.
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