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971.
For any α∈(0,2), a truncated symmetric α-stable process in ℝ
d
is a symmetric Lévy process in ℝ
d
with no diffusion part and with a Lévy density given by c|x|−d−α
1{|x|<1} for some constant c. In (Kim and Song in Math. Z. 256(1): 139–173, [2007]) we have studied the potential theory of truncated symmetric stable processes. Among other things, we proved that the boundary
Harnack principle is valid for the positive harmonic functions of this process in any bounded convex domain and showed that
the Martin boundary of any bounded convex domain with respect to this process is the same as the Euclidean boundary. However,
for truncated symmetric stable processes, the boundary Harnack principle is not valid in non-convex domains. In this paper,
we show that, for a large class of not necessarily convex bounded open sets in ℝ
d
called bounded roughly connected κ-fat open sets (including bounded non-convex κ-fat domains), the Martin boundary with respect to any truncated symmetric stable process is still the same as the Euclidean
boundary. We also show that, for truncated symmetric stable processes a relative Fatou type theorem is true in bounded roughly
connected κ-fat open sets.
The research of P. Kim is supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic
Research Promotion Fund) (KRF-2007-331-C00037).
The research of R. Song is supported in part by a joint US-Croatia grant INT 0302167. 相似文献
972.
Alexander I. Nazarov 《Journal of Global Optimization》2008,40(1-3):289-303
We describe recent results on attainability of sharp constants in the Sobolev inequality, the Sobolev–Poincaré inequality,
the Hardy–Sobolev inequality and related inequalities. This gives us the solvability of boundary value problems to critical
Emden–Fowler equations.
相似文献
973.
带干扰的多险种Cox风险模型的破产概率 总被引:1,自引:0,他引:1
考虑到保险公司在实际经营中收益所具有的不确定性和风险经营的多元化,建立了一个更现实的风险模型即带干扰的多险种Cox风险模型.运用鞅论得到了该模型最终破产概率的上界,并对Lundberg不等式作了推广. 相似文献
974.
有效不等式在整数规划的定界研究中具有重要的意义.研究了一般整数规划问题的有效不等式的升维方法,引入超加性函数给出同步升维的条件,并给出有效不等式的同步升维的具体方法,算例表明本文提出的方法是有效的. 相似文献
975.
976.
给出一类离散变量函数展开的方法,给出对Van der Corput不等式的一个改进;将这个方法扩展后可以应用于更多的离散变量函数的展开与研究,例如对Stirling公式的改进. 相似文献
977.
利用变分原理和Z2不变群指标研究了二阶常微分方程边值问题{u″(t)-u(t) f(t,u(t))=0,0<t<1,u′(0)=0,α1u(1) u′(1)=0,(其中α1>-1/2).得出了这类方程存在无穷个解的充分条件. 相似文献
978.
In the actuarial literature a lot of attention is given to the approximation of aggregate claims distributions by compound Poisson and Polya distributions and their subsequent numerical evaluation. The present contribution derives bounds for the tail of compound distributions and stop-loss premiums. The bounds are obtained in an elementary manner based on a version of the Chebyshev inequality. The main point of this contribution consists in deriving bounds with explicit dependence on the distribution function itself as well as on some partial moments of it. 相似文献
979.
Nobuo Inagaki Pranab Kumar Sen 《Annals of the Institute of Statistical Mathematics》1985,37(1):251-269
Summary The basic regularity conditions pertaining to the asymptotic theory of progressively truncated likelihood functions and maximum
likelihood estimators are considered, and the uniform strong consistency and weak convergence of progressively truncated maximum
likelihood estimators are studied systematically.
Work done during the first author's visit (as a visiting scholar) to the University of North Carolina at Chapel Hill, supported
by the Ministry of Education of the Japanese Government.
Work supported by the (U.S.) National Heart, Lung and Blood Institute, Contact NIH-NHLBI-F1-2243-L. 相似文献
980.
Pseudo-monotone complementarity problems in Hilbert space 总被引:1,自引:0,他引:1
In this paper, some existence results for a nonlinear complementarity problem involving a pseudo-monotone mapping over an arbitrary closed convex cone in a real Hilbert space are established. In particular, some known existence results for a nonlinear complementarity problem in a finite-dimensional Hilbert space are generalized to an infinite-dimensional real Hilbert space. Applications to a class of nonlinear complementarity problems and the study of the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions are given.This research was partially supported by the National Science Foundation Grant DMS-89-13089, Department of Energy Grant DE-FG03-87-ER-25028, and Office of Naval Research Grant N00014-89-J-1659. The authors would like to express their sincere thanks to Professor S. Schaible, School of Administration, University of California, Riverside, for his helpful suggestions and comments. They also thank the referees for their comments and suggestions that improved this paper substantially. 相似文献