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.
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页码：558 / 569
页数：12
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