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卷 27, 编号 3 (2017)
- 年: 2017
- 文章: 4
- URL: https://journals.rcsi.science/1055-1344/issue/view/12222
Article
On computable estimates for accuracy of approximation for the Bartlett–Nanda–Pillai statistic
摘要
For the Bartlett–Nanda–Pillai statistic, we find computable estimates for accuracy of approximation, i.e., we describe explicitly the dependence on all parameters of the distributions that occur in the inequalities. For the other two classical statistics traditionally used in multivariate analysis of variance, i.e., the likelihood-ratio and Lawley–Hotelling statistics, similar computable estimates were found earlier.
153-159
The large deviation principle for a compound Poisson process
摘要
For a compound Poisson process, under the moment Cramér condition, the extended large deviation principle is established in the space of functions of bounded variation with the Borovkov metric.
160-186
On integration of systems of stochastic differential equations
摘要
We suggest a method for solving systems of stochastic differential equations and describe the structure of solutions.
187-195
The spectrum of the Laplace operator on connected compact simple Lie groups of rank four
摘要
In the present article, we explicitly compute the spectrum of the Laplace operator on smooth real-valued and complex-valued functions on connected compact simple Lie groups of rank four with a bi-invariant Riemannian metrics that correspond to the root systems B4, C4, and D4. We also find a connection between the obtained formulas, number theory, and integral quadratic forms in two, three, and four variables.
196-226