A central limit theorem for integrals with respect to random measures

被引:0
作者
V. P. Demichev
机构
[1] Moscow State University,
来源
Mathematical Notes | 2014年 / 95卷
关键词
central limit theorem; integral with respect to a stationary random measure; Burgers equation with random initial data;
D O I
暂无
中图分类号
学科分类号
摘要
Integrals with respect to stationary random measures are considered. A central limit theorem for such integrals is proved. The results are applied to obtain a functional central limit theorem for transformed solutions of the Burgers equation with random initial data.
引用
收藏
页码:191 / 201
页数:10
相关论文
共 31 条
  • [1] Shandarin S F(1989)The large scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium Rev. Modern Phys. 61 185-220
  • [2] Zeldovich Ya B(1991)Asymptotical normality of a solution of Burgers’ equation with random initial data Teor. Veroyatnost. Primenen. 36 217-235
  • [3] Bulinskii A V(1992)CLT for the solution of the multidimensional Burgers equation with random data Ann. Acad. Sci. Fenn. Ser. A IMath. 17 11-22
  • [4] Molchanov S A(1995)Gibbs-Cox random fields and Burgers turbulence Ann. Appl. Probab. 5 461-492
  • [5] Bulinskii A V(1995)Limit theorems for solutions of the Burgers equation with Gaussian and non-Gaussian initial conditions Teor. Veroyatnost. Primenen. 40 387-403
  • [6] Funaki T(1995)Hyperbolic asymptotics in Burgers’ turbulence and extremal processes Comm. Math. Phys. 168 209-226
  • [7] Surgailis D(1991)Two results concerning asymptotic behaviour of solutions of the Burgers equation with force J. Stat. Phys. 64 1-12
  • [8] Woyczyński W A(2005)Burgers’ turbulence problem with linear or quadratic external potential J. Appl. Probab. 42 550-565
  • [9] Leonenko N(2006)Scaling laws for the multidimensional Burgers equation with quadratic external potential J. Stat. Phys. 124 191-205
  • [10] Orsingher E(2001)A functional central limit theorem for transformed solutions of the multidimensional Burgers equation with random initial data Teor. Veroyatnost. Primenen. 46 427-448