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81.
Here we investigate a majorization problem involving starlike function of complex order belonging to a certain class defined by means of fractional derivatives. Relevant connections of the main results obtained in this paper with those given by earlier workers on the subject are also pointed out. 相似文献
82.
We present here a systematic study of general boundary value problems on weighted networks that includes the variational formulation of such problems. In particular, we obtain the discrete version of the Dirichlet Principle and we apply it to the analysis of the inverse problem of identifying the conductivities of the network in a very general framework. Our approach is based on the development of an efficient vector calculus on weighted networks which mimetizes the calculus in the smooth case. The key tool is an adequate construction of the tangent space at each vertex. This allows us to consider discrete vector fields, inner products and general metrics. Then, we obtain discrete versions of derivative, gradient, divergence and Laplace-Beltrami operators, satisfying analogous properties to those verified by their continuous counterparts. On the other hand we develop the corresponding integral calculus that includes the discrete versions of the Integration by Parts technique and Green’s Identities. Finally, we apply our discrete vector calculus to analyze the consistency of difference schemes used to solve numerically a Robin boundary value problem in a square. 相似文献
83.
This paper is concerned with the final value problem associated with a linear operator A in a Banach space, where −A is the generator of a uniformly bounded analytic semigroup. Based on the deLaubenfels' functional calculus, we use new quasi-reversibility method, introduced by Boussetila and Rebbani recently, to form an approximate problem. We obtain some results in a Banach space similar to those in a Hilbert space. 相似文献
84.
Hoh 《Applied Mathematics and Optimization》2008,45(3):269-281
Pseudodifferential operators with negative definite symbols appear as generators of jump-type Markov processes. The purpose
of this paper is to treat the large jumps of the process by a perturbation approach for the generator. This is of particular
interest since in this way the generators are made accessible to a symbolic calculus of pseudodifferential operators. The
main auxiliary result consists of a characterization of tightness of the jump measures in terms of the symbol. 相似文献
85.
Jipu Ma 《Frontiers of Mathematics in China》2008,3(2):305-316
Let E and F be Banach spaces, f: U ⊂ E → F be a map of C
r
(r ⩾ 1), x
0 ∈ U, and ft (x
0) denote the FréLechet differential of f at x
0. Suppose that f′(x
0) is double split, Rank(f′(x
0)) = ∞, dimN(f′(x
0)) > 0 and codimR(f′(x
0)) s> 0. The rank theorem in advanced calculus asks to answer what properties of f ensure that f(x) is conjugate to f′(x
0) near x
0. We have proved that the conclusion of the theorem is equivalent to one kind of singularities for bounded linear operators,
i.e., x
0 is a locally fine point for f′(x) or generalized regular point of f(x); so, a complete rank theorem in advanced calculus is established, i.e., a sufficient and necessary condition such that the
conclusion of the theorem to be held is given.
相似文献
86.
We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov
transform for the the two-parameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity
theory.
相似文献
87.
米哈伊·列夫舍茨 《数学的实践与认识》2009,39(11)
基于代数和显式一致估计的微积分思想可以追溯到前牛顿时代,或者欧拉和拉格朗日.由于所涉及的数学非常简单,新的方法可以从一些简单的例子出发,直接、自然却严格地建立微分和积分的流线型理论,并不需要连续性、极限和紧性的概念. 相似文献
88.
We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and
a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends the results
proved in Klein et al. (Electron J Probab 11(20):27, 2006) in the one-dimensional case. We also study a geometric interpretation of convex ordering for discrete measures in connection
with the conditions set on the jump heights and intensities of the considered processes.
The work described in this paper was partially supported by a grant from City University of Hong Kong (Project No. 7200108). 相似文献
89.
We use Palm calculus to derive a simple, intuitive system of two linear-quadratic equations and two unknowns, whose algebraic solution yields Harel’s (1988) upper bound to the Erlang loss probability. We then derive a sequence of progressively stronger systems of equations, which eventually become exact. We provide two example applications. 相似文献
90.
Asian options are hard to price both analytically and numerically. Even though they have been the focus of much attention in recent years, there is no single technique which is widely accepted to price Asian options for all choices of market parameters. For hedging purposes, the estimation of the price sensitivities is often as important as the evaluation of the prices themselves. This paper provides a survey of current methods for pricing Asian options and computing their sensitivities to the key input parameters. The methods discussed include: Monte Carlo simulation, the finite difference approach and various quasi analytical approaches and approximations. We discuss practical numerical issues that arise in implementing these methods. The paper compares the accuracy and efficiency of the different approaches and offers some general conclusions. 相似文献