共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each a>0, let $\{Y^{(a)}_{n}:n\ge1\}In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts.
For each a>0, let {Y(a)n:n 3 1}\{Y^{(a)}_{n}:n\ge1\} be a sequence of independent and identically distributed random variables and {X(a)t:t 3 0}\{X^{(a)}_{t}:t\ge0\} be a Lévy process such that X1(a)=dY1(a)X_{1}^{(a)}\stackrel{d}{=}Y_{1}^{(a)},
\mathbbEX1(a) < 0\mathbb{E}X_{1}^{(a)}<0 and
\mathbbEX1(a)-0\mathbb{E}X_{1}^{(a)}\uparrow0 as a↓0. Let S(a)n=?k=1n Y(a)kS^{(a)}_{n}=\sum _{k=1}^{n} Y^{(a)}_{k}. Then, under some mild assumptions, , for some random variable and some function Δ(⋅). We utilize this result to present a number of limit theorems for suprema of Lévy processes in the
heavy-traffic regime. 相似文献
2.
We present the solutions of boundary-value and initial boundary-value problems for a nonlinear parabolic equation with Lévy
Laplacian ∆
L
resolved with respect to the derivative
\frac?U( t,x )?t = f( U( t,x ),DLU( t,x ) ) \frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {U\left( {t,x} \right),{\Delta_L}U\left( {t,x} \right)} \right) 相似文献
3.
S. S. Gribkova 《Journal of Mathematical Sciences》2010,167(4):506-511
Let x(t),t ? [ 0,1 ] \xi (t),t \in \left[ {0,1} \right] , be a jump Lévy process. By Px {\mathcal{P}_\xi } we denote the law of in the Skorokhod space
\mathbbD {\mathbb{D}} [0, 1]. Under some nondegeneracy condition on the Lévy measure Λ of the process, we construct a group of Px {\mathcal{P}_\xi } -preserving transformations of the space
\mathbbD {\mathbb{D}} [0, 1]. Bibliography: 10 titles. 相似文献
4.
Graziano Crasta Annalisa Malusa 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(2):129-150
We study the solvability of the minimization problem
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