共查询到20条相似文献,搜索用时 78 毫秒
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本文研究Besov空间上Riemann-Liouville型重分数布朗单的弱收敛问题.分别利用平面上的Poisson过程和两列独立的Riemann-Liouville型重分数布朗运动的部分和,构造了Riemann-Liouville型重分数布朗单的弱极限定理. 相似文献
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本文研究了当Hurst参数日小于1/2时关于分数布朗运动的随机积分问题.利用分数布朗运动的性质和卷积逼近的方法,获得了多重分数Stratonovich积分的另一种构造. 相似文献
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《应用数学与计算数学学报》2017,(4)
推导了分数阶积分的梯形逼近格式以及Caputo导数的L1逼近格式的四阶展开公式.并利用L1格式的展开式得到了Caputo导数的具有3-α阶精度的三点逼近格式,该逼近格式被应用于数值求解分数阶松弛方程和时间分数阶次扩散方程. 相似文献
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本文研究了多重分数斯特拉托诺维奇积分,通过卷积逼近技巧和分数布朗运动的随机积分的性质,构造了当Hurst参数小于二分之一时的多重随机积分.这种方法是新的不同于文[8]中的构造方法. 相似文献
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Naoto Kumano-go 《Bulletin des Sciences Mathématiques》2004,128(3):197-251
Using the time slicing approximation, we give a mathematically rigorous definition of Feynman path integrals for a general class of functionals on the path space. As an application, we prove the interchange with Riemann-Stieltjes integrals, the interchange with a limit, the perturbation expansion formula, the semiclassical approximation, and the fundamental theorem of calculus in Feynman path integral. 相似文献
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The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic. 相似文献
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Stefan Geiss 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):241-270
We approximate certain stochastic integrals, typically appearing in Stochastic Finance, by stochastic integrals over integrands, which are path-wise constant within deterministic, but not necessarily equidistant, time intervals. We ask for rates of convergence if the approximation error is considered in L 2 . In particular, we show that by using non-equidistant time nets, in contrast to equidistant time nets, approximation rates can be improved considerably. 相似文献
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C. Vinti 《Journal of Optimization Theory and Applications》1983,41(1):213-237
This paper is a survey on the integrals of the calculus of variations as Weierstrass integrals. While the classic integrals in terms of Lebesgue processes are valid only overAC curves, surfaces, or variety, the corresponding Weierstrass or Burkill integrals are valid in theBV case. This is the immediate advantage of the Weierstrass-Burkill form. Moreover, Cesari defined a very general integration process for set functions, in an abstract setting, which extends the Weierstrass and Burkill integrals. In more detail, we examine here some existence, approximation, representation, and semicontinuity results both in the parametric case and in the nonparametric case. 相似文献
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Naoto Kumano-go 《Bulletin des Sciences Mathématiques》2011,(8):936-987
We give two general classes of functionals for which the phase space Feynman path integrals have a mathematically rigorous meaning. More precisely, for any functional belonging to each class, the time slicing approximation of the phase space path integral converges uniformly on compact subsets with respect to the starting point of momentum paths and the endpoint of position paths. Each class is closed under addition, multiplication, translation, real linear transformation and functional differentiation. Therefore, we can produce many functionals which are phase space path integrable. Furthermore, though we need to pay attention for use, the interchange of the order with the integrals with respect to time, the interchange of the order with some limits, the semiclassical approximation of Hamiltonian type, the natural property under translation, the integration by parts with respect to functional differentiation, and the natural property under orthogonal transformation are valid in the phase space path integrals. 相似文献
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《Stochastic Processes and their Applications》2002,101(1):113-125
We study the simulation of stochastic processes defined as stochastic integrals with respect to type G Lévy processes for the case where it is not possible to simulate the type G process exactly. The type G Lévy process as well as the stochastic integral can on compact intervals be represented as an infinite series. In a practical simulation we must truncate this representation. We examine the approximation of the remaining terms with a simpler process to get an approximation of the stochastic integral. We also show that a stochastic time change representation can be used to obtain an approximation of stochastic integrals with respect to type G Lévy processes provided that the integrator and the integrand are independent. 相似文献
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《Journal of Complexity》2003,19(3):445-453
About 13 years ago we started collecting published cubature formulas for the approximation of multivariate integrals over some standard regions. In this paper we describe how we make this information available to a larger audience via the World Wide Web. 相似文献
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In addition to some new cubature formulas for the approximation of integrals over the unit disk, we present a survey of all known cubature formulas of algebraic degree for this region. 相似文献
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《Journal of Computational and Applied Mathematics》1998,89(2):257-261
For the numerical evaluation of finite-part integrals with singularities of order p ⩾ 1, we give error bounds for quadrature methods based on spline approximation. These bounds behave in the same way as the optimal ones. The ideas of the proof are also useful for methods based on other approximation processes. 相似文献