scholarly journals Tail distribution estimates of the mixed-fractional CEV model

2021 ◽  
Vol 5 (1) ◽  
pp. 371-379
Author(s):  
Nguyen Thu Hang ◽  
◽  
Pham Thi Phuong Thuy ◽  
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Malliavin Calculus ◽  
Explicit Estimate ◽  
Cev Model ◽  
Model Driven ◽  
Tail Distribution ◽  
Tail Distributions

The aim of this paper is to study the tail distribution of the CEV model driven by Brownian motion and fractional Brownian motion. Based on the techniques of Malliavin calculus and a result established recently in [<a href="#1">1</a>], we obtain an explicit estimate for tail distributions.

Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application

2020 ◽  
Vol 28 (4) ◽  
pp. 291-306
Author(s):  
Tayeb Bouaziz ◽  
Adel Chala
Keyword(s):  
Brownian Motion ◽  
Maximum Principle ◽  
Control Problem ◽  
Fractional Brownian Motion ◽  
Stochastic Control ◽  
Malliavin Calculus ◽  
Stochastic Maximum Principle ◽  
Hurst Parameter ◽  
Principle Of Optimality ◽  
Initial Cost

AbstractWe consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter {H\in(\frac{1}{2},1)} and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.

scholarly journals Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Yuquan Cang ◽  
Junfeng Liu ◽  
Yan Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Nonparametric Regression ◽  
Local Time ◽  
Kernel Function ◽  
Malliavin Calculus ◽  
Bandwidth Parameter ◽  
Subfractional Brownian Motion ◽  
Normal Law

We study the asymptotic behavior of the sequenceSn=∑i=0n-1K(nαSiH1)(Si+1H2-SiH2),asntends to infinity, whereSH1andSH2are two independent subfractional Brownian motions with indicesH1andH2, respectively.Kis a kernel function and the bandwidth parameterαsatisfies some hypotheses in terms ofH1andH2. Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motionSH1. We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.

scholarly journals Existence and regularity of the density for solutions of stochastic differential equations with boundary noise

2016 ◽  
Vol 19 (01) ◽  
pp. 1650007 ◽  
Author(s):  
Stefano Bonaccorsi ◽  
Margherita Zanella
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Lebesgue Measure ◽  
Malliavin Calculus ◽  
Nonlinear Term ◽  
Stochastic Perturbation ◽  
Heat Diffusion ◽  
Boundary Noise ◽  
Smooth Density

We study the existence and regularity of densities for the solution of a nonlinear heat diffusion with stochastic perturbation of Brownian and fractional Brownian motion type: we use the Malliavin calculus in order to prove that, if the nonlinear term is suitably regular, then the law of the solution has a smooth density with respect to the Lebesgue measure.

Stochastic calculus for fractional Lévy processes

2014 ◽  
Vol 17 (01) ◽  
pp. 1450006
Author(s):  
Kai He
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Malliavin Calculus ◽  
Lévy Processes ◽  
Stochastic Integral ◽  
Levy Processes ◽  
Stochastic Calculus

In this paper, we construct fractional Lévy processes for any parameter H ∈ (0, 1), as the generalization of the fractional Brownian motion. By using Malliavin calculus, we also define the stochastic integral for fractional Lévy processes.

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