In this paper, we study the existence and uniqueness of Hadamard Itô-Doob Stochastic Fractional Order Systems (HIDSFOS) using Picard iteration method. Different from previous works, our paper presents a new theory fractional integral. We have proved convergence solution averaged HIDSFOS to that standard in sense mean square also probability. Some examples are given at end illustrate theoretical...

Özet. Komuta kontrol bilgi sistemleri (KKBS), askeri organizasyonlar tarafından her türlü planlama, görevlendirme ve harekât faaliyetlerinin bütünleştirilmesi ve gerçekleştirilmesinin kolaylaştırılması amacıyla kullanılmaktadır. Her ne kadar farklı askeri organizasyonlar kendi KKBS’leri için farklı gereksinim kümeleri ortaya koysa da, tüm organizasyonlar için ortaklaştırılabilecek bir takım ger...

We study a stochastic complex Ginzburg–Landau (CGL) equation driven by a smooth noise in space and we establish exponential convergence of the Markov transition semi-group toward a unique invariant probability measure. Since Doob Theorem does not seem not to be useful in our situation, a coupling method is used. In order to make this method easier to understand, we first focus on two simple exa...

In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decomposition with respect to the super(sub)martingale introduced by this nonlinear expectation. Then we an application on the pricing of American options in incomplete market.

This article is devoted to showing the existence and uniqueness (EU) of a solution with non-Lipschitz coefficients (NLC) fractional Itô-Doob stochastic differential equations driven by countably many Brownian motions (FIDSDECBMs) order ϰ∈(0,1) using Picard iteration technique (PIT) semimartingale local time (SLT).