共查询到20条相似文献,搜索用时 15 毫秒
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Eric V. Slud 《Stochastic Processes and their Applications》1994,50(2):221-233
Let (Ω,
,P) be a probability space equipped with two filtrations {
t} and {
t} satisfying the usual conditions. Assume that X is a semimartingale and that h is locally bounded and predictable for each of the two filtrations {
t} and {
t}. New examples of such processes are given. Utilizing and extending partial results of Zheng (1982), this paper extends the available results on the relationship between the stochastic integral processes ∫ths dXs taken respectively in the sense of {
t} and of {
t}. In particular, it is shown that these stochastic integrals differ at most by a continuous process with quadratic variation defined and equal to 0. If both stochastic integrals are {
t∩
t} semimartingales, then it is proved that the stochastic integral ∫ths dX s taken in {
t} sense is indistinguishable from that taken in {
t} sense. 相似文献
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Lithuanian Mathematical Journal - 相似文献
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《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-4):269-284
Stochastic processes with values in a separable Frechet space whose a itinuous linear functional are real-valued square integrable martingales are investigated. The coordinate measures on the Fréchet space are obtained from cylinder set measures on a Hilbert space that is dense in the Fréchet space. Real-valued stochastic integrals are defined from the Fréchet-valued martingales using integrands from the topological dual of the aforementioned Hilbert space. An increasing process with values in the self adjoint operators on the Hilbert space plays a fundamental role in the definition of stochastic integrals. For Banach-valued Brownian motion the change of variables formula of K. Itô is generalized. A converse to the construction of the measures on the Fréchet space from cylinder set measures on a Hilbert space is also obtained. 相似文献
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In this paper we will consider the properties of various stochastic integrals over a complex valued, two parameter Wiener process. Integrals of this type exhibit pleasant features which do not appear within the real framework. They are stable under approximation and viewed in relation with analytic functions, they typically satisfy an ordinary chain rule. This in turn gives rise to several nice representation formulas. 相似文献
10.
Given an antisymmetric kernel K (K(z, z′) = ?K(z′, z)) and i.i.d. random variates Zn, n?1, such that EK2(Z1, Z2)<∞, set An = ∑1?i?j?nK(Zi,Zj), n?1. If the Zn's are two-dimensional and K is the determinant function, An is a discrete analogue of Paul Lévy's so-called stochastic area. Using a general functional central limit theorem for stochastic integrals, we obtain limit theorems for the An's which mirror the corresponding results for the symmetric kernels that figure in theory of U-statistics. 相似文献
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Extended Thorin classes and stochastic integrals 总被引:1,自引:1,他引:0
B. Grigelionis 《Lithuanian Mathematical Journal》2007,47(4):406-411
Extended Thorin classes T
ϰ
(R
d
), ϰ > 0, of infinitely divisible probability laws on R
d are defined and analytically characterized in [6]. Using general results from [8] and [9], in this paper, we derive a stochastic
integral representation of these classes.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 4, pp. 497–503, October–December, 2007. 相似文献
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Kazumasa Kuwada 《Probability Theory and Related Fields》2009,144(1-2):1-51
We prove a precision of large deviation principle for current-valued processes such as shown in Bolthausen et al. (Ann Probab 23(1):236–267, 1995) for mean empirical measures. The class of processes we consider is determined by the martingale part of stochastic line integrals of 1-forms on a compact Riemannian manifold. For the pair of the current-valued process and mean empirical measures, we give an asymptotic evaluation of a nonlinear Laplace transform under a nondegeneracy assumption on the Hessian of the exponent at equilibrium states. As a direct consequence, our result implies the Laplace approximation for stochastic line integrals or periodic diffusions. In particular, we recover a result in Bolthausen et al. (Ann Probab 23(1):236–267, 1995) in our framework. 相似文献
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A. V. Gorbunov 《Ukrainian Mathematical Journal》1994,46(4):449-453
We generalize the method for construction of operator stochastic integrals suggested by Berezanskii, Zhernakov, and Us. We extend the class of integrable commutative quantum processes and study properties of corresponding integrals.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 425–429, April, 1994.This work was partially supported by the Ukrainian State Committee on Science and Technology. 相似文献
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Michał Kisielewicz 《随机分析与应用》2018,36(3):495-520
The article is devoted to new properties of Aumann, Lebesgue, and Itô set-valued stochastic integrals considered in papers [1,2]. In particular, it contains some approximation theorems for Aumann and Itô set-valued stochastic integrals. Hence, in particular, it follows that Aumann and Lebesgue set-valued stochastic integrals cover a.s., both for measurable and IF-nonanticipative integrably bounded set-valued stochastic processes. 相似文献
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Adam Osekowski 《Proceedings of the American Mathematical Society》2008,136(8):2951-2958
Let be a nonnegative supermartingale and be a predictable process with values in . Let denote the stochastic integral of with respect to . The paper contains the proof of the sharp inequality where . A discrete-time version of this inequality is also established.