共查询到20条相似文献,搜索用时 156 毫秒
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《纯粹数学与应用数学》2016,(6)
讨论了一类带分数Brown运动的非Lipschitz增长的随机微分方程适应解的存在唯一性.关于分数Brown运动的随机积分有多种定义,本文使用一种广义Stieltjes积分定义方法,利用这种积分的性质,建立了一类由标准Brown运动和一个Hurst指数H∈(1/2,1)的分数Brown运动共同驱动的、系数为非Lipschitz增长的随机微分方程适应解的存在唯一性定理. 相似文献
2.
《数学物理学报(A辑)》2020,(1)
该文讨论了一类带分数Brown运动,且系数为局部线性增长的随机微分方程适应解的存在唯一性.使用一种广义tieltjes积分定义方法定义关于分数Brown运动的随机积分,利用这种积分的性质,得到了一类由标准Brown运动和一个Hurst指数H∈(1/2,1)的分数Brown运动共同驱动的、系数为局部线性增长的随机微分方程适应解的存在唯一性结果. 相似文献
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考虑如下一维双参数随机微分方程: ,其中{Wj,j=1,2,…}为一列无穷个相互独立的实值Brown单.作者定义关于无穷个Brown单的随机积分,并给出方程在非Lipschitz系数的条件下解的存在唯一性的一个结果. 相似文献
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利用不动点方法,研究了一类分数阶微分方程积分边值问题,在Lipschitz条件下,得到了非平凡解的存在唯一性,并给出唯一解的迭代序列.所得结论推广和改进了近期这方面的一些结果. 相似文献
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在积分型Lipschitz条件下,证明了一类以连续鞅为驱动的随机泛函微分方程解的存在性与唯一性. 相似文献
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本文在非Lipschitz系数下,考虑了一类多值的倒向随机微分方程.利用极大单调算子的Yosida估计和倒向随机微分方程在非Lipschitz条件下解的存在唯一性,获得了多值带跳的倒向随机微分方存在唯一解的结论. 相似文献
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研究了Hirst参数H>1/2分数Brown运动驱动的随机延迟微分方程(SDDE).随机积分如Duncan et al.[9]所定义的Wick-It(o)型随机积分,在系数具有充分正则性条件下,证明了随机延迟微分方程解的存在唯一性,其中利用了Malliavin φ-导数及随机分析. 相似文献
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本文研究一类由分数布朗运动驱动的一维倒向随机微分方程解的存在性与唯一性问题,在假设其生成元满足关于y Lipschitz连续,但关于z一致连续的条件下,通过应用分数布朗运动的Tanaka公式以及拟条件期望在一定条件下满足的单调性质,得到倒向随机微分方程的解的一个不等式估计,应用Gronwall不等式得到了一个关于这类方程的解的存在性与唯一性结果,推广了一些经典结果以及生成元满足一致Lipschitz条件下的由分数布朗运动驱动的倒向随机微分方程解的结果. 相似文献
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N. A. Kolodii 《Russian Mathematics (Iz VUZ)》2010,54(2):16-27
In this paper we study stochastic Volterra equations in a plane. These equations contain integrals with respect to fields
of locally bounded variation and square-integrable strong martingales. We prove the existence and the uniqueness of solutions
of such equations with locally integrable (in some measure) trajectories, assuming that the coefficients of equations possess
the Lipschitz property with respect to the functional argument. We prove that a solution of a stochastic Volterra integral
equation in a plane is continuous with respect to parameter. 相似文献
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In this paper, we consider complex-valued Brownian motion with p-adic time index and the associated abstract Wiener space. We define symmetric stochastic integrals with respect to p-adic Brownian motion. We also provide a sufficient condition for the existence of symmetric stochastic integrals and present a relation to the adjoint of the Malliavin derivatives. 相似文献
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In this paper, we shall firstly illustrate why we should introduce an It5 type set-valued stochastic differential equation and why we should notice the almost everywhere problem. Secondly we shall give a clear definition of Aumann type Lebesgue integral and prove the measurability of the Lebesgue integral of set-valued stochastic processes with respect to time t. Then we shall present some new properties, especially prove an important inequality of set-valued Lebesgue integrals. Finally we shall prove the existence and the uniqueness of a strong solution to the It5 type set-valued stochastic differential equation. 相似文献
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Marek T. Malinowski Mariusz Michta 《Journal of Mathematical Analysis and Applications》2012,394(1):30-47
We consider a notion of set-valued stochastic Lebesgue–Stieltjes trajectory integral and a notion of set-valued stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of set-valued stochastic integral equations. The existence and uniqueness of the solution to such the equations is proven. As a generalization of set-valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales. 相似文献
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《随机分析与应用》2013,31(4):755-782
In this paper, we use the Riemann sum approach to construct the anticipative stochastic integrals and consider the Cauchy problem (non-adapted initial value) for stochastic integral equations driven by discontinuous semimartingales. For general equations with Lipschitz coefficients, we prove the existence of the solutions. Apropos of semilinear equations, we find that under some conditions uniqueness of solutions will also hold. 相似文献
17.
Onno van Gaans 《Integral Equations and Operator Theory》2005,51(3):435-458
This paper considers semilinear stochastic differential equations in Hilbert spaces with Lipschitz nonlinearities and with the noise terms driven by sequences of independent scalar Wiener processes (Brownian motions). The interpretation of such equations requires a stochastic integral. By means of a series of Itô integrals, an elementary and direct construction of a Hilbert space valued stochastic integral with respect to a sequence of independent scalar Wiener processes is given. As an application, existence and strong and weak uniqueness for the stochastic differential equation are shown by exploiting the series construction of the integral. 相似文献
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In this paper, we first study the existence and uniqueness of solutions to the stochastic differential equations driven by fractional Brownian motion with non-Lipschitz coefficients. Then we investigate the explosion time in stochastic differential equations driven by fractional Browmian motion with respect to Hurst parameter more than half with small diffusion. 相似文献
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本文研究了算子值过程关于Gel’fand三元组EHE*上Lévy过程的随机积分.利用再生核Hilbert空间上柱Lévy过程的随机积分,定义一类算子值过程关于E*-值Lévy过程的随机积分。 相似文献
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Antoine Lejay 《Journal of Differential Equations》2010,249(8):1777-1798
The theory of rough paths allows one to define controlled differential equations driven by a path which is irregular. The most simple case is the one where the driving path has finite p-variations with 1?p<2, in which case the integrals are interpreted as Young integrals. The prototypal example is given by stochastic differential equations driven by fractional Brownian motion with Hurst index greater than 1/2. Using simple computations, we give the main results regarding this theory - existence, uniqueness, convergence of the Euler scheme, flow property … - which are spread out among several articles. 相似文献