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令X是连续半鞅 ,f是R上的局部可积函数 .本文我们将证明 ,只要∫t0 f(Xs)ds存在 ,那么平方协变差存在且等于 - ∫Rf(a)daLat,Lta是X的局部时 .因此对具有导数 f的绝对连续函数F ,有推广的It 公式F(Xt) =F(X0 ) + ∫t0 f(Xs)dXs+ 12 [f(X) ,X]t. 相似文献
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Spatiotemporal propagation dynamics of intense optical pulses in loosely confined gas-filled hollow-core fibers 下载免费PDF全文
We numerically study the propagation dynamics of intense optical pulses in gas-filled hollow-core fibers(HCFs). The spatiotemporal dynamics of the pulses show a transition from tightly confined to loosely confined characteristics as the fiber core is increased, which manifests as a deterioration in the spatiotemporal uniformity of the beam. It is found that using the gas pressure gradient does not enhance the beam quality in large-core HCFs, while inducing a positive chirp in the pulse to lower the peak power can improve the beam quality. This indicates that the self-focusing effect in the HCFs is the main driving force for the propagation dynamics. It also suggests that pulses at longer wavelengths are more suitable for HCFs with large cores because of the lower critical power of self-focusing, which is justified by the numerical simulations. These results will benefit the generation of energetic few-cycle pulses in large-core HCFs. 相似文献
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设{Wt.Ft.t∈[0,T]}为概率空间(Ω,F,P)上的标准α维Brownfcfc,Ft为由它生成的自然σ-代数流。本文讨论了如下随机微分方程终值问题弱解的存在性:Xt=ξ+∫t^Tg(s,Xs,Ys)ds+∫t^TYsdWs其中ξ∈L^2(Ω,FT,P;R^n),g:[0,T]×R^n×Rnd→R^n为有界可测函数。此外,还讨论了它在金融市场期权定价问题中的应用。 相似文献
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本文扼要介绍量子随机分析的某些最新发展。在第一部分,阐述了量子概率论的vonNeumann公理系统,并把它与经典概率论的公理系统作了比较。第二部分介绍Fock空间上的基本运算及Fock空间的各种概率解释。最后一部分介绍了由Hudson和Parthasarathy建立并引起大家注意的非交换随机分析理论。 相似文献
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自从 Wiener 1923年构造了 Brown 运动的数学模型以来,许多人试图对 Wiener 泛函建立一套分析理论.不幸的是,许多常见的泛函,例如 It积分或 It方程的解,相对于 Wiener空间的任何一种 Banach 范数来说,未必都是连续的,当然更谈不上它们的 Fréchet 微分了.直到 1976年,Malliavin 建立了一套对 Wiener 泛函的“相对微分”运算,使这些重要的泛函在某种意义下是“光滑”的,因而获得了一个重大的突破.由于这种微分运算是对 Wiener 相似文献
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对于用(n十1)x(。+l)个点组成的空间点阵r‘少==(x‘,,y‘J,习.J) (落=0,l,…,n;夕’二0,1,…,11盆),给出其边界点的外端斜率(切矢量)户。,,户。,,r,.。,r几。(1)(1)声(j=O,阴;乞=0,l,…,n)以后“·”与“,”分别表示对变数、与叨的求导。现在对每一个固定的落(=o,1,一,”),我们用三次样条曲线8于来拟合。+l个点及其端点斜率 r二。,同时,对每一个固定的j(=O,l,端点斜率r,。,r一,,…,r‘二,r二,,一,nl),我们用三次样条曲线泞梦来拟合n十l个点及其 户。,,roJ,r,夕,…,r。,,户。夕。于是所有的 召于,‘于 (艺二0,1,…,n,j=0,1,…,m)构成了以(… 相似文献
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Generation of few-cycle radially-polarized infrared pulses in a gas-filled hollow-core fiber 下载免费PDF全文
We perform a numerical study for temporally compressing radially-polarized(RP) infrared pulses in a gas-filled hollow-core fiber(HCF). The dynamic transmission and nonlinear compression of RP pulses centered at wavelengths of0.8 m, 1.8 m, 3.1 m, and 5.0 m in HCFs are simulated. By comparing the propagation of pulses with the same optical cycles and intensity, we find that under proper conditions these pulses can be compressed down to 2–3 cycles. In the transverse direction, the spatiotemporal beam profile ameliorates from 0.8-m to 1.8-m and 3.1-m pulses before the appearance of high-order dispersion. These results show an alternative method of scaling generation for delivering RP infrared pulses in gas-filled HCFs, which can obtain energetic few-cycle pulses, and will be beneficial for relevant researches in the infrared scope. 相似文献