Stochastic integrals and stochastic equations in set-valued and fuzzy-valued frameworks

被引：2

作者：

Michta, Mariusz ^{[1
]}

机构：

[1] Univ Zielona Gora, Fac Math Comp Sci & Econometr, Szafrana 4A, PL-65516 Zielona Gora, Poland

来源：

STOCHASTICS AND DYNAMICS | 2020年 / 20卷 / 01期

关键词：

Set-valued function; fuzzy set; set-valued stochastic integral; fuzzy stochastic integral; set-valued stochastic differential equation; fuzzy stochastic differential equation; DIFFERENTIAL-EQUATIONS; REPRESENTATION; INCLUSIONS; MULTIFUNCTIONS; INTERRELATION; STABILITY; EXISTENCE; THEOREMS; DRIVEN; SPACES;

D O I：

10.1142/S021949372050001X

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：

In this paper, we study the existence, uniqueness and properties of solutions to set-valued and fuzzy-valued stochastic differential equations with respect to finite variation and martingale integrators. We present new types of such equations that generalize those studied earlier. For this aim we introduce properly defined new types of stochastic integrals in set-valued and fuzzy-valued settings and we establish their main properties. The results obtained in the paper generalize conclusions dealing with this topic known both in deterministic and stochastic cases.

引用

页数：47

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