Inequalities for the moments of stochastic integrals and stochastic Volterra equations driven a two-parameter wiener process

被引:0
作者
N. A. Kolodii
机构
[1] Volgograd State University,
来源
Siberian Mathematical Journal | 2013年 / 54卷
关键词
two-parameter Wiener process; stochastic Volterra equation; stopping line;
D O I
暂无
中图分类号
学科分类号
摘要
We prove existence and uniqueness theorems for a solution to a stochastic Volterra equation on the plane. The proofs employ an inequality for a stochastic integral with respect to a two-parameter Wiener process, where the integrand depends on the limits of integration.
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页码:829 / 840
页数:11
相关论文
共 12 条
[1]  
Gushchin A A(1982)On the general theory of random fields on the plane Russian Math. Surveys 37 55-80
[2]  
Dozzi M(1991)Twoparameter stochastic processes Math. Res. 61 17-43
[3]  
Klepcina M L(1984)On strong solutions of stochastic Itô-Volterra equations Theory Probab. Appl. 29 154-158
[4]  
Veretennikov A Yu(1990)Stochastic Volterra equations with anticipating coefficients Ann. Probab. 18 1635-1655
[5]  
Pardoux E(1991)The Davis inequalities and the Gundy decomposition for two-parameter strong martingales. I Theory Probab. Math. Stat. 42 29-37
[6]  
Protter P(1978)Calcul stochastique d’ependant d’un parametre Z. Wahrsch. Verw. Gebiete Bd45 109-133
[7]  
Gushchin A A(2000)On existence of continuous modifications of random processes Theory Stoch. Process. 6 54-57
[8]  
Mishura Yu S(1996)Gronwall-Bellman type integral inequalities in measure spaces J. Math. Anal. Appl. 202 183-193
[9]  
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