scholarly journals Topological method for coupled systems of impulsive stochastic semilinear differential inclusions with fractional Brownian motion

2019 ◽  
Vol 20 (1) ◽  
pp. 71-106 ◽  
Author(s):  
T. Blouhi ◽  
◽  
T. Caraballo ◽  
A. Ouahab ◽  
◽  
...  
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Differential Inclusions ◽  
Coupled Systems ◽  
Topological Method

scholarly journals Set-Valued Functions of Bounded Generalized Variation and Set-Valued Young Integrals

2020 ◽  
Author(s):  
Mariusz Michta ◽  
Jerzy Motyl
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Differential Inclusions ◽  
Stochastic Integrals ◽  
Stochastic Differential Inclusions ◽  
Generalized Variation

AbstractThe paper deals with some properties of set-valued functions having bounded Riesz p-variation. Set-valued integrals of Young type for such multifunctions are introduced. Selection results and properties of such set-valued integrals are discussed. These integrals contain as a particular case set-valued stochastic integrals with respect to a fractional Brownian motion, and therefore, their properties are crucial for the investigation of solutions to stochastic differential inclusions driven by a fractional Brownian motion.

scholarly journals Selection Properties and Set-Valued Young Integrals of Set-Valued Functions

2020 ◽  
Vol 75 (4) ◽  
Author(s):  
Mariusz Michta ◽  
Jerzy Motyl
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Differential Inclusions ◽  
Stochastic Integrals ◽  
Hölder Continuous ◽  
Stochastic Differential Inclusions ◽  
Different Types ◽  
Convexity Assumptions

AbstractThe paper deals with some selection properties of set-valued functions and different types of set-valued integrals of a Young type. Such integrals are considered for classes of Hölder continuous or with bounded Young p-variation set-valued functions. Two different cases are considered, namely set-valued functions with convex values and without convexity assumptions. The integrals contain as a particular case set-valued stochastic integrals with respect to a fractional Brownian motion, and therefore, their properties are crucial for the investigation of solutions to stochastic differential inclusions driven by a fractional Brownian motion.

scholarly journals A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm

2014 ◽  
Vol 51 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Dawei Hong ◽  
Shushuang Man ◽  
Jean-Camille Birget ◽  
Desmond S. Lun
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Fractional Brownian Motion ◽  
Parallel Algorithm ◽  
Uniform Approximation ◽  
Haar Wavelets ◽  
Hurst Index ◽  
Sample Paths ◽  
Vanishing Moment ◽  
Uniform Expansion

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1] of Hurst index H ∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

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