PROBABILISTIC APPROXIMATION OF THE SOLUTION OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER SCHRODINGER EQUATION

被引：1

作者：

Platonova, M., V ^{[1
,2
]}

Tsykin, S., V ^{[3
]}

机构：

[1] Russian Acad Sci, St Petersburg Dept, Steklov Math Inst, St Petersburg 191023, Russia

[2] St Petersburg State Univ, Chebyshev Lab, St Petersburg 199034, Russia

[3] St Petersburg State Univ, St Petersburg 199034, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2021年 / 65卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

Schrodinger equation; Poisson random measure; limit theorems;

D O I：

10.1137/S0040585X97T990125

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We propose two methods of approximation of the solution of the Cauchy problem for the higher-order Schrodinger equation. In the first method, the expectation of a functional of some random point field is used, and in the second, the expectation of a functional of the normed sums of independent and identically distributed random variables with finite moment of order 2m + 2 is employed.

引用

页码：558 / 569

页数：12

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