共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, we study the existence and (Hölder) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that in one dimension and in the rough case , the Hölder exponent (in ) of the local time is , where is the Hurst parameter of the driving fractional Brownian motion. 相似文献
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In this paper, by using a Taylor type development, we show how it is possible to associate differential operators with stochastic differential equations driven by fractional Brownian motions. As an application, we deduce that invariant measures for such SDE’s must satisfy an infinite dimensional system of partial differential equations. 相似文献
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We prove the Malliavin regularity of the solution of a stochastic differential equation driven by a fractional Brownian motion of Hurst parameter H>0.5. The result is based on the Fréchet differentiability with respect to the input function for deterministic differential equations driven by Hölder continuous functions. It is also shown that the law of the solution has a density with respect to the Lebesgue measure, under a suitable nondegeneracy condition. 相似文献
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In this paper linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion are studied. A necessary and sufficient condition for the existence and uniqueness of the solution is established and the spatial regularity of the solution is analyzed; separate proofs are required for the cases of Hurst parameter above and below 1/2. The particular case of the Laplacian on the circle is discussed in detail.
Mathematics Subject Classification (2000): 60H15, 60G15 相似文献
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A time fractional functional differential equation driven by the fractional Brownian motion 下载免费PDF全文
Let $B^H$ be a fractional Brownian motion with Hurst index $H>\frac12$. In this paper, we prove the global existence and uniqueness of the equation
$$
\begin{cases}
^CD_t^{\gamma}x(t)=f(x_t)+G(x_t)\frac{d}{dt}B^H(t),\ \ \ \ &t\in(0,T], \x(t)=\eta(t), \ \ \ \ \ &t\in[-r,0],
\end{cases}
$$
where $\max\{H,2-2H\}<\gamma<1$, $^CD_t^{\gamma}$ is the Caputo derivative, and $x_t\in \mathcal{C}_r=\mathcal{C}([-r,0],\mathbb{R})$ with $x_t(u)=x(t+u),u\in[-r,0]$. We also study the dependence of the solution on the initial condition. 相似文献
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Francesca Biagini Yaozhong Hu Bernt
ksendal Agns Sulem 《Stochastic Processes and their Applications》2002,100(1-2):233-253
We prove a stochastic maximum principle for controlled processes X(t)=X(u)(t) of the formwhere B(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter
. As an application we solve a problem about minimal variance hedging in an incomplete market driven by fractional Brownian motion. 相似文献
dX(t)=b(t,X(t),u(t)) dt+σ(t,X(t),u(t)) dB(H)(t),
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In this paper we give a sufficient condition for the exponential asymptotic behavior of solutions of a general class of linear fractional stochastic differential equations with time-varying delays. Our obtained results allow us to employ the theories developed for the deterministic systems and to illustrate this, some examples are provided. 相似文献
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冉启康 《纯粹数学与应用数学》2016,32(6):551-561
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
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By using regularization approximations of the underlying subordinator and a gradient estimate approach, the dimension-independent Harnack inequalities are established for the inhomogeneous semigroup associated with a class of SDEs with Lévy noise containing a subordinate Brownian motion. Our estimates in Harnack type inequalities improve the corresponding ones in the recent paper by Wang and Wang (2014) [10]. 相似文献
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Guolian Wang Ming Zeng Boling Guo 《Journal of Mathematical Analysis and Applications》2010,371(1):210-222
In this paper, we consider the stochastic Burgers' equation driven by a genuine cylindrical fractional Brownian motion with Hurst parameter . We first prove the regularities of the solution to the linear stochastic problem corresponding to the stochastic Burgers' equation. Then we obtain the local and global existence and uniqueness results for the stochastic Burgers' equation. 相似文献
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Xiliang FAN 《Frontiers of Mathematics in China》2015,10(3):595
This paper is devoted to study a class of stochastic Volterra equations driven by fractional Brownian motion. We first prove the Driver type integration by parts formula and the shift Harnack type inequalities. As a direct application, we provide an alternative method to describe the regularities of the law of the solution. Secondly, by using the Malliavin calculus, the Bismut type derivative formula is established, which is then applied to the study of the gradient estimate and the strong Feller property. Finally, we establish the Talagrand type transportation cost inequalities for the law of the solution on the path space with respect to both the uniform metric and the L2-metric. 相似文献
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Yinghan Zhang 《Stochastics An International Journal of Probability and Stochastic Processes》2016,88(3):415-427
In this paper, we consider the stochastic elastic equation driven by a cylindrical fractional Brownian motion. The regularities of the solution to the linear stochastic problem corresponding to the stochastic elastic equation are proved. Then, we obtain the existence of the solution using the Picard iteration. 相似文献
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Kexue Li 《Mathematical Methods in the Applied Sciences》2015,38(8):1582-1591
In this paper, we consider a class of stochastic delay fractional evolution equations driven by fractional Brownian motion in a Hilbert space. Sufficient conditions for the existence and uniqueness of mild solutions are obtained. An application to the stochastic fractional heat equation is presented to illustrate the theory. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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B. L. S. Prakasa Rao 《随机分析与应用》2019,37(2):271-280
We discuss nonparametric estimation of trend coefficient in models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with small noise. 相似文献