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本文求出了Brown运动关于圆柱面的首中点分布,解决了圆柱体上的Dirichlet问题。 相似文献
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设D为Rd中的有界规则区域.本文绘出了一个D内条件Brown运动生命时的渐近估计其中G为Rd内满足的开集,为主持征值(关于Dirichlet边值条件),μ是属于广义Kato类的符号Radon测度,At是与μ相联系的Brown运动(Xt)t≥0的有界变差连续的可加泛函,h是关D内的正解。 相似文献
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设{W(t):t∈R},{B(t):t∈R+}是两相互独立取值于R且W(0)=B(0)=0的标准Brown运动,{Y(t)=W(B(t)),t∈R+}为R上的重Brown运动,X1(t),…,Xd(t)是Y(t)的d个独立复制.我们将探讨d维重Brown运动X(t)=(X1(t),…,Xd(t))的像集和图集的精确Hausdorff测度.更确切地,得到了X的像集X(Q)={X(t):t∈Q}和图集GrX(Q)={(t,X(t)):t∈Q}的精确Hausdorff测度,其中Q为(0,∞)上的Borel集. 相似文献
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设{W(t):t∈R},{B(t):t∈R }是两相互独立取值于R且W(0)= B(0)=0的标准Brown运动, {Y(t)=W(B(t)),t∈R }为R上的重Brown运动,X1(t),…,Xd(t)是Y(t)的d个独立复制.我们将探讨d维重Brown运动X(t)=(X1(t),…,Xd(t))的像集和图集的精确Hausdorff测度.更确切地,得到了X的像集X(Q)={X(t):t∈Q}和图集GrX(Q)={(t,X(t)):t∈Q}的精确Hausdorff测度,其中Q为(0,∞)上的Borel集. 相似文献
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设{W(t): t∈R}, {B(t): t∈R+}是两相互独立取值于R且W(0)=B(0)=0的标准Brown运动, {Y(t)=W(B(t)), t∈R+}为RR上的重Brown运动,X1(t), ..., Xd(t)是Y(t)的d个独立复制. 我们将探讨d维重Brown运动X(t)=(X1(t), ..., Xd(t))的像集和图集的精确 Hausdorff 测度. 更确切地, 得到了X 的像集X(Q)={X(t): t∈Q}$和图集GrX(Q)={(t, X(t)): t∈Q}的精确Hausdorff 测度, 其中Q为(0, ∞)上的Borel 集. 相似文献
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设X=(Xt)t≥0为R^d中的标准Brown运动,Br=(x:x∈R^d,/x/〈r)为以原点中心,半径r的球,分别用Lr,Tr及Tr表示X末遇Br,首出Br及停留在Br中的时间,本文给出了求这些变量的矩的一般公式,并求出了前二阶矩。 相似文献
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本文给出了从球外任一点出发的布朗运动的极大游程的几种不同的定义,求出了极大游程的分布,以及极大游程与首达极大时的联合分布,作为推论求出了首达极大时的分布. 相似文献
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Sierpinski gasket上Brown运动k重时的Hausdorff维数 总被引:1,自引:0,他引:1
吴军 《数学年刊A辑(中文版)》1996,(3)
设k≥2是正整数{X(t),t≥0}是SierpinskigasketG上的Brown运动,本文研究了{X(t),t≥0}k重时的Hausdorff维数,证明了:其中Mk={(t1,t2…,tk)}∈Rk:t1,t2,…,tk互不相同,使得X(t1)=X(t2)=…=X(tk)}, 相似文献
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AsymptoticBehaviorforHittingTimeofLargeGeodesicSpheresbyBrownianMotionWangFengyu(王凤雨)(DepartmentofMathematics.Beijing,100875)... 相似文献
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Yimin Xiao 《Journal of Theoretical Probability》1998,11(2):383-408
Let {W(t), tR} and {B(t), t0} be two independent Brownian motions in R with W(0) = B(0) = 0 and let
be the iterated Brownian motion. Define d-dimensional iterated Brownian motion by
where X
1, X
d are independent copies of Y. In this paper, we investigate the existence, joint continuity and Hölder conditions in the set variable of the local time
of X(t), where
is the Borel -algebra of R
+. These results are applied to study the irregularities of the sample paths and the uniform Hausdorff dimension of the image and inverse images of X(t). 相似文献
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利用Ito公式及Ito积分的性质求出了布朗运动和几何布朗运动的矩的一般形式,同时指出可以利用这种方法求其他扩散过程的矩. 相似文献
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Abstract We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration and the classical Itô stochastic calculus. The existence result is based on the Yamada–Watanabe theorem. 相似文献
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With appropriate regularity assumptions on the increasing concave function x=(t)<0, the hitting time density p(t) for a transient curve x=(t) by a 1-dimensional Brownian motion is shown to satisfy
Here r is the probability of eventually hitting the curve and (t)=t
–1/2(t). 相似文献
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The solutions of various problems in the theories of queuing processes, branching processes, random graphs and others require the determination of the distribution of the sojourn time (occupation time) for the Brownian excursion. However, no standard method is available to solve this problem. In this paper we approximate the Brownian excursion by a suitably chosen random walk process and determine the moments of the sojourn time explicitly. By using a limiting approach, we obtain the corresponding moments for the Brownian excursion. The moments uniquely determine the distribution, enabling us to derive an explicit formula. 相似文献
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Periodica Mathematica Hungarica - 相似文献
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A cost process is associated with a discrete time, finite state Markov chain. Using backward recursion, the distribution of the first time the cost falls below a given level is calculated. 相似文献
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