Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases. When the drift is zero, we show that in the one-parameter case the solution in an exponential, thus positive, function while in the two-parameter settings t...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

Abstract We consider decoupling inequalities for random variables taking values in a Banach space X . restrict the class of distributions that appear as conditional while and show each adapted process can be approximated by Haar-type expansion which only pre-specified appear. Moreover, we our framework progressive enlargement underlying filtration does not affect properties (in particular, it c...

Abstract We study the asymptotic behavior of normalized maxima real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation chaos: in large population limit, behave as those arising an i.i.d. system where each particle follows associated McKean–Vlasov limiting dynamics. Because maximum depends on all particles, our does not follow from classical cha...

It is shown how to construct a successful co-adapted coupling of two copies of an n-dimensional Brownian motion (B1, . . . ,Bn) while simultaneously coupling all corresponding copies of Lévy stochastic areas ∫ Bi dBj − ∫ Bj dBi. It is conjectured that successful coadapted couplings still exist when the Lévy stochastic areas are replaced by a finite set of multiply iterated pathand time-integral...

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases. When the drift is zero, we show that in the one-parameter case the solution in an exponential, thus positive, function while in the two-parameter settings t...