Fuzzy Itand#244; Integral Driven by a Fuzzy Brownian Motion

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

A Note on Fuzzy Set–Valued Brownian Motion

In this paper, we prove that a fuzzy set–valued Brownian motion Bt, as defined in [2], can be handle by an R–valued Wiener process bt, in the sense that Bt = Ibt ; i.e. it is actually the indicator function of a Wiener process.

Adding Fuzzy Integral to Fuzzy Control

Sugeno integral was invented a few decades ago as a natural fuzzy-number analogue of the classical integral. Sugeno integral has many interesting applications. It is reasonable to expect that it can be used in all application areas where classical integrals are used, and in many such areas it is indeed useful. Surprisingly, however, it has never been used in fuzzy control, although in tradition...

Chaotic Behavior in Differential Equations Driven by a Brownian Motion

In this paper, we investigate the chaotic behavior of ordinary differential equations with a homoclinic orbit to a dissipative saddle point under an unbounded random forcing driven by a Brownian motion. We prove that, for almost all sample pathes of the Brownian motion in the classical Wiener space, the forced equation admits a topological horseshoe of infinitely many branches. This result is t...

A singular stochastic differential equation driven by fractional Brownian motion∗

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter H > 1 2 . Under some assumptions on the drift, we show that there is a unique solution, which has moments of all orders. We also apply the techniques of Malliavin calculus to prove that the solution has an absolutely continuous law at any time t > 0.