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

共 50 条

[41] The Cauchy problem for the fourth-order Schrodinger equation in Hs
Liu, Xuan
Zhang, Ting
JOURNAL OF MATHEMATICAL PHYSICS, 2021, 62 (07)
[42] Solution of the Cauchy problem for a time-dependent Schrodinger equation
Meiler, Maria
Cordero-Soto, Ricardo
Suslov, Sergei K.
JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (07)
[43] THE CAUCHY PROBLEM FOR THE SOBOLEV TYPE EQUATION OF HIGHER ORDER
Zamyshlyaeva, A. A.
Bychkov, E. V.
BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2018, 11 (01): : 5 - 14
[44] Limit theorems for symmetric random walks and probabilistic approximation of the Cauchy problem solution for Schrodinger type evolution equations
Ibragimov, I. A.
Smorodina, N. V.
Faddeev, M. M.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2015, 125 (12) : 4455 - 4472
[45] An inverse problem for a higher-order parabolic equation
V. L. Kamynin
E. Franchini
Mathematical Notes, 1998, 64 : 590 - 599
[46] An inverse problem for a higher-order parabolic equation
Kamynin, VL
Franchini, E
MATHEMATICAL NOTES, 1998, 64 (5-6) : 590 - 599
[47] GOURSAT PROBLEM FOR MANGERON EQUATION OF HIGHER-ORDER
OGUZTORELI, MN
BULLETIN DE LA CLASSE DES SCIENCES ACADEMIE ROYALE DE BELGIQUE, 1972, 58 (04): : 464 - +
[48] Approximation to the Dirichlet problem for a higher-order elliptic equation with a spectral parameter and a discontinuous nonlinearity
Potapov, D. K.
DIFFERENTIAL EQUATIONS, 2007, 43 (07) : 1031 - 1032
[49] Approximation to the Dirichlet problem for a higher-order elliptic equation with a spectral parameter and a discontinuous nonlinearity
D. K. Potapov
Differential Equations, 2007, 43 : 1031 - 1032
[50] Exact soliton solutions for the higher-order nonlinear Schrodinger equation
Li, B
INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2005, 16 (08): : 1225 - 1237

← 1 2 3 4 5 →