On a class of Ito stochastic differential equations

被引：0
作者：
Romeo Negrea
机构：
[1] Politehnica University of Timisoara,Department of Mathematics
来源：
Rendiconti del Circolo Matematico di Palermo Series 2 | 2023年 / 72卷
关键词：
Stochastic differential equations; Pathwise uniqueness of the solutions; Fixed point theory method; Brownian motion; 45G10; 60H10; 60H20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We provide sufficient conditions on the drift and on the diffusion coefficients of Ito-type equations for the existence of stochastic-process solutions, constructed by successive approximations and which converge almost surely or in the mean-square. We also obtain a result for the uniqueness of the solutions, extending the classical theorem of Ito and consistent with respect to more recent pathwise uniqueness results. In particular, a relaxation of the Lipschitz condition is given by allowing a suitably controlled growth in the time-variable.
引用
收藏
页码：253 / 272
页数：19
相关论文
共 32 条
[1]  
Anguraj A(2021)On stability of stochastic differential equations with random impulses driven by Poisson jumps Stochastics 93 682-696
[2]  
Ravikumar K(1990)Uniqueness and convergence of successive approximations for ordinary differential equations Math. Jpn. 35 351-367
[3]  
Nieto JJ(1995)Global existence of solutions for perturbed differential equations Annali di Matematica Pura ed Applicata 168 237-299
[4]  
Athanassov ZS(1996)On the existence and pathwise uniqueness of solutions of stochastic differential equations Stoch. Stoch. Rep. 56 227-239
[5]  
Constantin A(2010)On Nagumo’s theorem Proc. Japan Acad. Ser. A Math. Sci. 86 41-44
[6]  
Constantin A(2004)An application of Schauder’s fixed point theorem in stochastic McShane modeling J. Fixed Point Theory 5 37-52
[7]  
Constantin A(1978)Pathwise uniqueness for solutions of systems differential equations Stoch. Processes Their Appl. 6 253-260
[8]  
Constantin Gh(1951)On stochastic differential equations Mem. Am. Math. Soc. 4 1-5
[9]  
Negrea R(2012)Some remarks on Nagumo’s theorem Czechoslovak Math. J. 62 235-242
[10]  
Gard TC(1926)Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichingen erster Ordung Jpn. J. Math. 3 107-112
1234