共查询到20条相似文献,搜索用时 0 毫秒
1.
Kimberly K. J. Kinateder Patrick McDonald 《Proceedings of the American Mathematical Society》1997,125(6):1815-1822
Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.
2.
A history of variational principles is presented through theirapplications to linear models arising from the theory of electromagnetism.This historical survey is enriched by some original contribution. 相似文献
3.
Victor H. de la Peñ a Patrick McDonald 《Proceedings of the American Mathematical Society》2004,132(8):2465-2474
Let be a one-dimensional diffusion with infinitesimal generator given by the operator where is a smooth, positive real-valued function and the ratio of and is a constant. Given a compact interval, we prove a Weierstrass-type theorem for the exit time moments of and their corresponding (naturally weighted) first derivatives, and we provide an algorithm that produces uniform approximations of arbitrary continuous functions by exit time moments. We investigate analogues of these results in higher-dimensional Euclidean spaces. We give expansions for several families of special functions in terms of exit time moments.
4.
Kimberly K. J. Kinateder Patrick McDonald 《Proceedings of the American Mathematical Society》1997,125(8):2453-2462
Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.
5.
Toshihiro Uemura 《数学学报(英文版)》2010,26(1):185-192
We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the process, while the precise expression of the (L^2-)generator of the Dirichlet form associated with the process is used to obtain the lower bounds. 相似文献
6.
本文根据文献[1],对非线性应力应变关系的弹性体,导出了弹性动力学问题的变分原理和广义变分原理,提出了混合位移协调元和混合应力协调元的瞬时广义变分原理. 相似文献
7.
First exit time distributions for multidimensional processes are key quantities in many areas of risk management and option pricing. The aim of this paper is to provide a flexible, fast and accurate algorithm for computing the probability of the first exit time from a bounded domain for multidimensional diffusions. First, we show that the probability distribution of this stopping time is the unique (weak) solution of a parabolic initial and boundary value problem. Then, we describe the algorithm which is based on a combination of the sparse tensor product finite element spaces and an hp-discontinuous Galerkin method. We illustrate our approach with several examples. We also compare the numerical results to classical Monte Carlo methods. 相似文献
8.
本文应用构造函数理论得到线弹性微孔材料的广义变分原理,得到构造函数与广义变分原理之间的对应关系. 相似文献
9.
Journal of Optimization Theory and Applications - 相似文献
10.
Ruzeng Zhu 《中国科学A辑(英文版)》1999,42(5):546-551
The differential variational principles of second kind for non-holonomic mechanics are given, from which a number of integral
variational principles of second kind are set up. From the latter, the general relation of δq′-δq and the general form of integral variational principles of the first kind and intermediate kinds are derived. Thus not only
all previous relations of δq′-δq and integral variational principles are unified but also the existance of the variational principles of intermediate kinds
are pointed out.
Project supported by the National Natural Science Foundation of China (Grant No. 19272064). 相似文献
11.
K. K. J. Kinateder Patrick McDonald David Miller 《Probability Theory and Related Fields》1998,111(4):469-487
Let X
t
be a diffusion in Euclidean space. We initiate a study of the geometry of smoothly bounded domains in Euclidean space using
the moments of the exit time for particles driven by X
t
, as functionals on the space of smoothly bounded domains. We provide a characterization of critical points for each functional
in terms of an overdetermined boundary value problem. For Brownian motion we prove that, for each functional, the boundary
value problem which characterizes critical points admits solutions if and only if the critical point is a ball, and that all
critical points are maxima.
Received: 23 January 1997 / Revised version: 21 January 1998 相似文献
12.
Jiyeon Lee 《Mathematical Methods of Operations Research》2007,65(1):169-178
An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. For this dam, we solve Kolmogorov’s
backward differential equation to obtain the Laplace transforms of the first exit times in terms of a certain positive kernel.
This allows us to provide an explicit expression for the Laplace transform of the wet period for a finite dam. 相似文献
13.
M. Hasanov 《Acta Appl Math》2002,71(2):117-126
An approximation method, based on a theorem on approximating general operator-valued functions by piecewise-linear ones, is presented and analyzed. Using this method, variational characteristics of the spectrum of a class of operator functions are established. 相似文献
14.
详细介绍了如何应用凑合反推法(semi-inverse method)构造弹性理论中的两类独立变量的广义变分原理(包括熟知的Hellinger-Reissner变分原理,Hu-Washizu变分原理)及三类独立变量的广义变分原理(钱伟长广义变分原理) 。应用凑合反推法还可以清楚地看出各变量之间的约束关系,从而再一次证明了Hu-Washizu变分原理实际上是两类独立变量的广义变分原理。 相似文献
15.
《Optimization》2012,61(9):1119-1132
We present two extensions of Korpelevich's extragradient method for solving the variational inequality problem (VIP) in Euclidean space. In the first extension, we replace the second orthogonal projection onto the feasible set of the VIP in Korpelevich's extragradient method with a specific subgradient projection. The second extension allows projections onto the members of an infinite sequence of subsets which epi-converges to the feasible set of the VIP. We show that in both extensions the convergence of the method is preserved and present directions for further research. 相似文献
16.
This paper investigates the first exit time and the ruin time of a risk reserve process with reserve-dependent income under the assumption that the claims arrive as a Poisson process. We show that the Laplace transform of the distribution of the first exit time from an interval satisfies an integro-differential equation. The exact solution for the classical model and for the Embrechts–Schmidli model are derived. 相似文献
17.
The steady-state simulation of a gas transmission network involves the solution of a system of nonlinear algebraic equations subject to a set of inequality constraints. The purpose of this paper is to consider how the problem can be cast into a variational inequality framework using the dual extremum principles described by Noble and Sewell in 1972. The reliability of the model is tested on two networks supplied by the British Gas Corporation. 相似文献
18.
Harry Kesten R. A. Maller 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》1999,35(6):685
We show that the passage time, T*(r), of a random walk Sn above a horizontal boundary at r (r≥0) is stable (in probability) in the sense that
as r→∞ for a deterministic function C(r)>0, if and only if the random walk is relatively stable in the sense that
as n→∞ for a deterministic sequence Bn>0. The stability of a passage time is an important ingredient in some proofs in sequential analysis, where it arises during applications of Anscombe's Theorem. We also prove a counterpart for the almost sure stability of T*(r), which we show is equivalent to E|X|<∞, EX>0. Similarly, counterparts for the exit of the random walk from the strip {|y|≤r} are proved. The conditions arefurther related to the relative stability of the maximal sum and the maximum modulus of the sums. Another result shows that the exit position of the random walk outside the boundaries at ±r drifts to ∞ as r→∞ if and only if the random walk drifts to ∞. 相似文献
19.
In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example. 相似文献
20.
Starting from recent strong and weak approximations to the partial sums of i.i.d. random vectors (cf. U. Einmahl, Ann. Probab., 15 1419–1440), some corresponding invariance principles are developed for associated renewal processes and random sums. Optimality of the approximation is proved in the case when only two moments exist. Among other applications, a Darling-Erdös type extreme value theorem for renewal processes will be derived. 相似文献