共查询到20条相似文献,搜索用时 30 毫秒
1.
Let X, X1 , X2 , . . . be i.i.d. random variables, and set Sn = X1 +···+Xn , Mn = maxk≤n |Sk|, n ≥1. Let an = o( (n)(1/2)/logn). By using the strong approximation, we prove that, if EX = 0, VarX = σ2 0 and E|X| 2+ε ∞ for some ε 0, then for any r 1, lim ε1/(r-1)(1/2) [ε-2-(r-1)]∞∑n=1 nr-2 P{Mn ≤εσ (π2n/(8log n))(1/2) + an } = 4/π . We also show that the widest a n is o( n(1/2)/logn). 相似文献
2.
Yuexu Zhao 《Bulletin of the Brazilian Mathematical Society》2006,37(3):377-391
Let X1, X2, ... be i.i.d. random variables with EX1 = 0 and positive, finite variance σ2, and set Sn = X1 + ... + Xn. For any α > −1, β > −1/2 and for κn(ε) a function of ε and n such that κn(ε) log log n → λ as n ↑ ∞ and
, we prove that
*Supported by the Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. 20060237 and 20050494). 相似文献
3.
Nils Svanstedt 《Applications of Mathematics》2010,55(5):385-404
Stochastic homogenization (with multiple fine scales) is studied for a class of nonlinear monotone eigenvalue problems. More
specifically, we are interested in the asymptotic behaviour of a sequence of realizations of the form
$
- div\left( {a\left( {T_1 \left( {\frac{x}
{{\varepsilon _1 }}} \right)\omega _1 ,T_2 \left( {\frac{x}
{{\varepsilon _2 }}} \right)\omega _2 ,\nabla u_\varepsilon ^\omega } \right)} \right) = \lambda _\varepsilon ^\omega \mathcal{C}\left( {u_\varepsilon ^\omega } \right)
$
- div\left( {a\left( {T_1 \left( {\frac{x}
{{\varepsilon _1 }}} \right)\omega _1 ,T_2 \left( {\frac{x}
{{\varepsilon _2 }}} \right)\omega _2 ,\nabla u_\varepsilon ^\omega } \right)} \right) = \lambda _\varepsilon ^\omega \mathcal{C}\left( {u_\varepsilon ^\omega } \right)
相似文献
4.
D. V. Goryashin 《Moscow University Mathematics Bulletin》2011,66(3):125-128
For the number N(x) of solutions to the equation aq − bc = 1 in positive integers a, b, c and square-free numbers q satisfying the condition aq ≤ x the asymptotic formula
|