Fuzzy and Set-Valued Stochastic Differential Equations with Solutions of Decreasing Fuzziness

被引：5
|
作者：
Malinowski, Marek T. [1 ]
机构：
[1] Univ Zielona Gora, Fac Math Comp Sci & Econometr, PL-65516 Zielona Gora, Poland
来源：
STRENGTHENING LINKS BETWEEN DATA ANALYSIS AND SOFT COMPUTING | 2015年 / 315卷
关键词：
Fuzzy stochastic differential equation; fuzzy stochastic integral equation; set-valued stochastic differential equation; ITO TYPE;
D O I：
10.1007/978-3-319-10765-3_13
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
We consider fuzzy stochastic differential equations in a new formulation. The equations that we examine possess solutions which are the fuzzy stochastic processes with trajectories of decreasing fuzziness in their consecutive values. This is a novelty. We give a theorem that guarantees existence and uniqueness of solutions. Some fuzzy stochastic differential equations are solved explicitly and some visualizations of simulations connected with their solutions are included. All the results can be applied immediately to set-valued stochastic differential equations.
引用
收藏
页码：105 / 112
页数：8
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