The Laplace method for probability measures in Banach spaces
The Laplace method for probability measures in Banach spaces
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Banach 空间中概率测度的拉普拉斯方法
DOI：
10.1070/rm1995v050n06abeh002635
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发表时间：
1995
影响因子：
0.9
通讯作者：
V. Fatalov
中科院分区：
文献类型：
--
作者：
V. Piterbarg;V. Fatalov
内容§1。第1章Banach空间中依赖于大参数的连续积分的渐近分析。连续积分的大偏差原理及对数渐近性。巴拿赫空间中高斯积分的精确渐近性：拉普拉斯方法3.1。高斯积分的拉普拉斯方法占据了整个希尔伯特空间：孤立最小点（[167]，I） 3.2。希尔伯特空间高斯积分的拉普拉斯方法：极小点流形（[167]，II） 3.3。Banach空间中高斯积分的拉普拉斯方法（[90],[174],[176]）高斯模的大偏差的精确渐近性§4。Banach空间中有值的独立随机元素和分布的拉普拉斯方法非简并最小点的情况（[137]，I） 4.2。简并孤立极小点和极小点的流形（[137]，II）§5。进一步的例子5.1。马尔可夫对称过程的局部时间泛函的拉普拉斯方法[217]5.2。扩散过程的拉普拉斯方法，有限个数的非退化极小点（[116]）5.3。霍尔德范数中布朗运动大偏差的渐近性Hilbert空间中一个强稳定律的非渐近展开式（[41]）二重和法——连续函数空间中拉普拉斯方法的一个版本§6。匹肯兹的双和法6.2.一般情况高斯平稳过程最大值分布的渐近性高斯非平稳过程大偏移概率的渐近性§7。高斯场轨迹大偏差的概率7.1。均匀场和恒定色散场有限多色散最大值7.3。最大分散点的流形Wiener域的最大值分布的渐近性§8。空间中值为高斯向量和过程范数大偏差的精确渐近性。1 . Hilbert空间中具有参数集的高斯场8.1具有相关坐标的有限维高斯向量-范数分布的精确渐近性，1$ SRC=http://ej.iop.org/images/0036-0279/50/6/R02/tex_rm_2635_img4.gif/> 8.2。8.3型过程轨迹高漂移概率的精确渐近性。Hilbert空间中具有一组参数的高斯过程的大偏差概率的渐近性[74]。值高斯过程规范最大值分布的渐近性8.5。数值Ornstein-Uhlenbeck过程大偏差的精确渐近性
Contents §1. Introduction Chapter I. Asymptotic analysis of continual integrals in Banach space, depending on a large parameter §2. The large deviation principle and logarithmic asymptotics of continual integrals §3. Exact asymptotics of Gaussian integrals in Banach spaces: the Laplace method 3.1. The Laplace method for Gaussian integrals taken over the whole Hilbert space: isolated minimum points ([167], I) 3.2. The Laplace method for Gaussian integrals in Hilbert space: the manifold of minimum points ([167], II) 3.3. The Laplace method for Gaussian integrals in Banach space ([90], [174], [176]) 3.4. Exact asymptotics of large deviations of Gaussian norms §4. The Laplace method for distributions of sums of independent random elements with values in Banach space 4.1. The case of a non-degenerate minimum point ([137], I) 4.2. A degenerate isolated minimum point and the manifold of minimum points ([137], II) §5. Further examples 5.1. The Laplace method for the local time functional of a Markov symmetric process ([217]) 5.2. The Laplace method for diffusion processes, a finite number of non-degenerate minimum points ([116]) 5.3. Asymptotics of large deviations for Brownian motion in the Holder norm 5.4. Non-asymptotic expansion of a strong stable law in Hilbert space ([41]) Chapter II. The double sum method - a version of the Laplace method in the space of continuous functions §6. Pickands' method of double sums 6.1. General situations 6.2. Asymptotics of the distribution of the maximum of a Gaussian stationary process 6.3. Asymptotics of the probability of a large excursion of a Gaussian non-stationary process §7. Probabilities of large deviations of trajectories of Gaussian fields 7.1. Homogeneous fields and fields with constant dispersion 7.2. Finitely many maximum points of dispersion 7.3. Manifold of maximum points of dispersion 7.4. Asymptotics of distributions of maxima of Wiener fields §8. Exact asymptotics of large deviations of the norm of Gaussian vectors and processes with values in the spaces and . Gaussian fields with the set of parameters in Hilbert space 8.1 Exact asymptotics of the distribution of the -norm of a Gaussian finite-dimensional vector with dependent coordinates, 1$ SRC=http://ej.iop.org/images/0036-0279/50/6/R02/tex_rm_2635_img4.gif/> 8.2. Exact asymptotics of probabilities of high excursions of trajectories of processes of type 8.3. Asymptotics of the probabilities of large deviations of Gaussian processes with a set of parameters in Hilbert space [74] 8.4. Asymptotics of distributions of maxima of the norms of -valued Gaussian processes 8.5. Exact asymptotics of large deviations for the -valued Ornstein-Uhlenbeck process Bibliography
反对称 Malliavin 微积分及其应用
DOI：
--
发表时间：
2007
期刊：
影响因子：
--
作者：
大江貴司;大中幸三郎;赤堀 次郎;M. Ikehata and T. Ohe;赤堀 次郎;K. Ohnaka;Jiro Akahori
通讯作者：
Jiro Akahori