[1]胡华.奇异线性随机微分方程的几个结果[J].江西师范大学学报(自然科学版),2015,(04):345-350.
 HU Hua.The Several Results of Singular Linear Stochastic Differential Equations[J].,2015,(04):345-350.
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奇异线性随机微分方程的几个结果()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2015年04期
页码:
345-350
栏目:
出版日期:
2015-07-01

文章信息/Info

Title:
The Several Results of Singular Linear Stochastic Differential Equations
作者:
胡华
宁夏大学数学计算机学院,宁夏 银川,750021
Author(s):
HU Hua
关键词:
随机微分方程Volterra变换布朗运动扩张滤过Goursat内核自再生核
Keywords:
stochastic differential equationsVolterra transformBrownian motionenlargement of filtrationsGour-sat kernelsself-reproducing kernels
分类号:
O211.6
文献标志码:
A
摘要:
研究了1类带有Goursat型核函数保留了维纳测度的Volterra变换,这类核函数满足自再生性。给出了几个能引起新的自再生性的相关Gram矩阵逆的结果,以及它与经典自再生性的联系。结果被应用于1类带相应滤过分解的奇异线性随机微分方程研究,研究的方程被看作是一些广义桥的非标准分解。
Abstract:
The type with Goursat kernel function retained the Wiener measure on the Volterra transformation is stud-ied. This kind of kernel function satisfy a self-reproduction property. Some results on the inverses of the associated Gramian matrices which lead to a new self-reproduction property are provided. And it links with the classical repro-duction property. The result is applied to a class of singular linear stochastic differential equation with corresponding filter decomposition’s study. The equation is regarded as some non-standard decomposition of generalized bridges.

参考文献/References:

[1] Jeulin Th,Yor M.Grossissements de filtrations:exemples et applications [M].Berlin:Springer-Verlag,1985.
[2] Deheuvels P.Invariance of Wiener processes and of Brownian bridges by integral transforms and applications [J].Stochastic Process Appl,1982,13(3):311-318.
[3] Jeulin Th,Yor M.Filtration des ponts browniens et equations differentielles lineaires [M].Berlin:Springer-Verlag,1990.
[4] Karatzas I,Pikovsky I.Anticipative portfolio optimization [J].Adv Appl Probab,1996,28(4):1095-1122.
[5] Kumaresan N.Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular fuzzy system with cross-term using neural networks [J].Neural Computing and Applications,2012,21(3):497-503.
[6] 任磊,孙乐平.一类奇异微分代数系统的数值解 [J].江西师范大学学报:自然科学版,2012,36(5):491-494.
[7] Kallianpur G.Stochastic filtering theory [M].New York:Springer-Verlag,1980.
[8] 包立平.一类奇摄动线性随机微分方程边值问题 [J].杭州电子科技大学学报,2012,32(1):92-95.
[9] 全晓静,韩惠丽,王健.Adomian分解法求解非线性分数阶Volterra积分方程 [J]..江西师范大学学报:自然科学版,2014,38(5):517-520.
[10] Berlinet A,Thomas-Agnan C.Reproducing kernel Hilbert spaces in probability and statistics [M].Boston:Kluwer Academic Publishers,2004.
[11] Hibino Y,Hitsuda M,Muraoka H.Construction of non-canonical representations of a Brownian motion [J].Hiroshima Math J,1997,27(3):439-448.
[12] Alili L.Canonical decomposition of certain generalized Brownian bridges [J].Electron Comm Probab,2002(7):27-36.
[13] Follmer H,Wu C T,Yor M.On weak Brownian motions of arbitrary order [J].Ann Inst H Poincare Probab Statist,2000,36(4):447-487.
[14] Protter Ph.Stochastic integration and differential equations [M].2nd ed.Berlin:Springer-Verlag,2005.
[15] Yor M.Some aspects of Brownian motion part I:some special functionals,lectures in mathematics ETH Zürich [M].Boston:Birkhäuser,1992.
[16] Baudoin F.Conditioned stochastic differential equations:theory,examples and application to finance [J].Stochastic Process Appl,2002,100(1/2):109-145.
[17] Amendinger J.Initial enlargement of filtrations and additional information in financial markets [D].Berlin:Technische Universitat,1999.

备注/Memo

备注/Memo:
国家自然科学基金(11361044)
更新日期/Last Update: 1900-01-01