共查询到16条相似文献,搜索用时 171 毫秒
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在本文里,我们定义了高维布朗运动的面局部时和有界区域的边界局部时,并用 Dirichlet 形式与随机分析理论证明布朗运动的面局部时对应的光滑测度正好是超平面上的面测度.作为上述结果的应用,我们还得到高维布朗运动可加泛函关于局部时的表示定理. 相似文献
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针对定解区域是无界区域的Dirichlet外问题,提出了一种新的有效的概率数值方法,它是从解的随机表达式出发,将无界区域上的问题转化成区域边界上的问题.此时,只要在边界上进行剖分,将问题离散化,然后在无界区域外的有界区域内构作一个辅助球,并且利用布朗运动、漂移布朗运动从球外一点出发,首中球面的位置和时间的分布等,就可以获得Dirichlet外问题的数值解. 相似文献
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本文利用经典的白噪声分析框架研究布朗运动和分数布朗运动混合的局部时.利用白噪声分析方法证明该局部时是一个Hida广义泛函.进一步,借助于S-变换给出了该局部时的混沌表示.本文所获得结果推广了GUO等(2011)获得的分数布朗运动情形下的一些结果. 相似文献
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在本文里,我们定义了高维布朗运动的面局部时和有界区域的边界局部时,并用 Dirichlet 形式与随机分析理论证明布朗运动的面局部时对应的光滑测度正好是超平面上的面测度.作为上述结果的应用,我们还得到高维布朗运动可加泛函关于局部时的表示定理. 相似文献
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非线性飘移布朗运动的极值分布 总被引:1,自引:0,他引:1
本文研究了从x出发的非线性漂移布朗运动的极大值、极小值和首达时问题.利用测度变换以及布朗运动的一些重要性质,如反射原理,增量的独立性等,获得了两种极值分布函数的精确表达式,得到了首达时的分布函数.结果表明,线性漂移布朗运动的极大值极小值以及首达时的分布问题的有关结果是本文结论的推论,最后给出一个例子. 相似文献
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This paper establish a first passage time model based
on the Merton's structural model by using the method of geometric Brownian
motion. In this paper, we consider the accounting noise and historical default
record and then introduce a new incomplete information hypothesis. Besides,
we introduce the stock's liquidity value into the model, and apply its method
measurement which based on Merton's structural model to the first passage
time model to obtain the endogenous default boundary. Based on the incomplete
information, the conditional default probability is derived by using the
default boundary. And at the last of this passage, we analysis the effect
of the correlation between stock's price and company assets on the default
probability. 相似文献
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在几何布朗运动假设基础上利用实物期权方法分析了不确定环境下农业用地向城市用地转化问题,得到了地价结构函数,同时利用首次达到时间理论分析了这一问题的可达性,并进行了比较静态分析,最后通过在转化开发前后征收不同税率分析了税收对土地转化和地价的影响.研究加深了我们对土地转化开发中的各种经济现象的理解和认识,并为房地产开发中的科学决策提供了理论支持. 相似文献
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Let t be a continuous Markov chain on N states. Consider adjoining a Brownian motion with this Markov chain so that the drift and the variance take different values when t is in different states. This new process Zt is a hidden Markov process. We study the probability distribution of the first passage time for Zt.Our result, when applied to the stock market, provides an explicit mathematical interpretation of the fact that in finite time, there is positive probability for the bull (bear) market to become bear (bull). 相似文献
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We propose a new approach to calculating the first passage time densities for Brownian motion crossing piecewise linear boundaries which can be discontinuous. Using this approach we obtain explicit formulas for the first passage densities and show that they are continuously differentiable except at the break points of the boundaries. Furthermore, these formulas can be used to approximate the first passage time distributions for general nonlinear boundaries. The numerical computation can be easily done by using the Monte Carlo integration, which is straightforward to implement. Some numerical examples are presented for illustration. This approach can be further extended to compute two-sided boundary crossing distributions. 相似文献
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Conditions on the boundary and parameters that produce ordering in the first passage time distributions of two different diffusion processes are proved making use of comparison theorems for stochastic differential equations. Three applications of interest in stochastic modeling are presented: a sensitivity analysis for diffusion models characterized by means of first passage times, the comparison of different diffusion models where first passage times represent an important feature and the determination of upper and lower bounds for first passage time distributions. 相似文献