A discrete stochastic Gronwall lemma

被引：15

作者：

Kruse, Raphael ^{[1
]}

Scheutzow, Michael ^{[1
]}

机构：

[1] Tech Univ Berlin, Inst Math, Str 17 Juni 136, DE-10623 Berlin, Germany

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2018年 / 143卷

关键词：

Gronwall lemma; Martingale inequality; Backward Euler-Maruyama method; A priori estimate;

D O I：

10.1016/j.matcom.2016.07.002

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The purpose of this paper is the derivation of a discrete version of the stochastic Gronwall lemma involving a martingale. The proof is based on a corresponding deterministic version of the discrete Gronwall lemma and an inequality bounding the supremum in terms of the infimum for discrete time martingales. As an application the proof of an a priori estimate for the backward Euler-Maruyama method is included. (C) 2016 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：149 / 157

页数：9

共 10 条

[1]

Banuelos R., 2014, ILLINOIS J MATH, V58, P149

[2] MORE GENERALIZED DISCRETE GRONWALL-INEQUALITIES [J].

BEESACK, PR .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1985, 65 (12) :589-595

[3]

Bellman R., 1943, Duke Math. J, V10, P643, DOI DOI 10.1215/S0012-7094-43-01059-2

[4]

Emmrich E., 1999, PREPRINT

[5]

Gronwall TH, 1918, ANN MATH, V20, P292

[6]

Holt J, 2009, NY TIMES BK REV, P8

[7]

Kloeden PE, 1999, Numerical Solution of Stochastic Differential Equations, Stochastic Modelling and Applied Probability

[8]

Milstein G. N., 1995, NUMERICAL INTEGRATIO

[9] A STOCHASTIC GRONWALL LEMMA [J].

Scheutzow, Michael .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2013, 16 (02)

[10]

[No title captured]

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