scholarly journals DEFINITION, PROPERTIES AND WAVELET ANALYSIS OF MULTISCALE FRACTIONAL BROWNIAN MOTION

Fractals ◽  
2007 ◽  
Vol 15 (01) ◽  
pp. 73-87 ◽  
Author(s):  
JEAN-MARC BARDET ◽  
PIERRE BERTRAND
Keyword(s):  
Brownian Motion ◽  
Wavelet Analysis ◽  
Fractional Brownian Motion ◽  
Long Memory ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Model Data ◽  
Fractional Brownian Motions ◽  
Piecewise Constant ◽  
Functional Central Limit

In some applications, for instance, finance, biomechanics, turbulence or internet traffic, it is relevant to model data with a generalization of a fractional Brownian motion for which the Hurst parameter H is dependent on the frequency. In this contribution, we describe the multiscale fractional Brownian motions which present a parameter H as a piecewise constant function of the frequency. We provide the main properties of these processes: long-memory and smoothness of the paths. Then we propose a statistical method based on wavelet analysis to estimate the different parameters and prove a functional Central Limit Theorem satisfied by the empirical variance of the wavelet coefficients.

scholarly journals Some Sequential Boundary Crossing Results for Geometric Brownian Motion and Their Applications in Financial Engineering

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Tristan Guillaume
Keyword(s):  
Brownian Motion ◽  
Financial Markets ◽  
Financial Engineering ◽  
Constant Function ◽  
Geometric Brownian Motion ◽  
Boundary Crossing ◽  
Piecewise Constant Function ◽  
Piecewise Constant ◽  
Option Contracts ◽  
Look Back

This paper provides new explicit results for some boundary crossing distributions in a multidimensional geometric Brownian motion framework when the boundary is a piecewise constant function of time. Among their various possible applications, they enable accurate and efficient analytical valuation of a large number of option contracts traded in the financial markets belonging to the classes of barrier and look-back options.

scholarly journals Current-phase relation in layered superconducting structures of SIS’IS type

2021 ◽  
Vol 24 (2) ◽  
pp. 23701
Author(s):  
A. M. Shutovskyi ◽  
V. E. Sakhnyuk
Keyword(s):  
Phase Difference ◽  
Current Density ◽  
Phase Relation ◽  
Dielectric Layer ◽  
Intermediate Layer ◽  
Order Parameter ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Current Phase ◽  
Piecewise Constant

The dependence of the current density on the phase difference is investigated considering the layered superconducting structures of a SIS’IS type. To simplify the calculations, the quasiclassical equations for the Green’s functions in a t-representation are derived. An order parameter is considered as a piecewise constant function. To consider the general case, no restrictions on the dielectric layer transparency and the thickness of the intermediate layer are imposed. It was found that a new analytical expression for the current-phase relation can be used with the aim to obtain a number of previously known results arising in particular cases.

scholarly journals Existence and Stability of Solutions of Fuzzy Fractional Stochastic Differential Equations with Fractional Brownian Motions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Elhoussain Arhrrabi ◽  
M’hamed Elomari ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Stability Of Solutions ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Existence And Stability ◽  
Fractional Stochastic Differential Equations

The existence, uniqueness, and stability of solutions to fuzzy fractional stochastic differential equations (FFSDEs) driven by a fractional Brownian motion (fBm) with the Lipschitzian condition are investigated. Finally, we investigate the exponential stability of solutions.

scholarly journals Continuous CM-regularity of semihomogeneous vector bundles

2020 ◽  
Vol 20 (3) ◽  
pp. 401-412
Author(s):  
Alex Küronya ◽  
Yusuf Mustopa
Keyword(s):  
Vector Bundle ◽  
Abelian Variety ◽  
Upper Bound ◽  
Vector Bundles ◽  
Projective Variety ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Piecewise Constant ◽  
Generic Vanishing

AbstractWe ask when the CM (Castelnuovo–Mumford) regularity of a vector bundle on a projective variety X is numerical, and address the case when X is an abelian variety. We show that the continuous CM-regularity of a semihomogeneous vector bundle on an abelian variety X is a piecewise-constant function of Chern data, and we also use generic vanishing theory to obtain a sharp upper bound for the continuous CM-regularity of any vector bundle on X. From these results we conclude that the continuous CM-regularity of many semihomogeneous bundles — including many Verlinde bundles when X is a Jacobian — is both numerical and extremal.

scholarly journals PERIODIC ORBITS OF SINGLE NEURON MODELS WITH INTERNAL DECAY RATE 0 < Β ≤ 1

2013 ◽  
Vol 18 (3) ◽  
pp. 325-345 ◽  
Author(s):  
Aija Anisimova ◽  
Maruta Avotina ◽  
Inese Bula
Keyword(s):  
Dynamical System ◽  
Decay Rate ◽  
Single Neuron ◽  
Discrete Dynamical System ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Sigmoid Function ◽  
Signal Function ◽  
Neuron Models ◽  
Piecewise Constant

In this paper we consider a discrete dynamical system x n+1=βx n – g(x n ), n=0,1,..., arising as a discrete-time network of a single neuron, where 0 &lt; β ≤ 1 is an internal decay rate, g is a signal function. A great deal of work has been done when the signal function is a sigmoid function. However, a signal function of McCulloch-Pitts nonlinearity described with a piecewise constant function is also useful in the modelling of neural networks. We investigate a more complicated step signal function (function that is similar to the sigmoid function) and we will prove some results about the periodicity of solutions of the considered difference equation. These results show the complexity of neurons behaviour.

On wavelet analysis of the nth order fractional Brownian motion

2012 ◽  
Vol 21 (3) ◽  
pp. 251-277
Author(s):  
Hedi Kortas ◽  
Zouhaier Dhifaoui ◽  
Samir Ben Ammou
Keyword(s):  
Brownian Motion ◽  
Wavelet Analysis ◽  
Fractional Brownian Motion

scholarly journals The Kirchhoff Transformation and the Fick’s Second Law with Concentration-dependent Diffusion Coefficient

2021 ◽  
Vol 16 ◽  
pp. 59-67
Author(s):  
R. M. S. Gama ◽  
R. Pazetto S. Gama
Keyword(s):  
Diffusion Coefficient ◽  
Mathematical Structure ◽  
Constant Function ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Piecewise Constant Function ◽  
Second Law ◽  
Piecewise Constant ◽  
Numerical Examples ◽  
Kirchhoff Transformation

In this work it is considered the Fick’s second law in a context in which the diffusion coefficient depends on the concentration. It is employed the Kirchhoff transformation in order to simplify the mathematical structure of the Fick’s second law, giving rise to a more convenient description. In order to provide a general protocol, the diffusion coefficient will be assumed a piecewise constant function of the concentration. Exact formulas are presented for both the Kirchhoff transformation and its inverse, in such a way that there is no limit of accuracy. Some numerical examples are presented with the aid of a semi-implicit procedure associated with a finite difference approximation.

scholarly journals A Production Inventory Model for deteriorating items with backlog-dependent demand

2019 ◽  
Author(s):  
Chayanika Rout ◽  
Debjani Chakraborty ◽  
Prof Adrijit Goswami
Keyword(s):  
Inventory Model ◽  
Constant Function ◽  
Deteriorating Items ◽  
Piecewise Constant Function ◽  
High Quality ◽  
Piecewise Constant ◽  
Production Inventory ◽  
Demand Rate ◽  
Theoretical Results ◽  
Dependent Demand

This paper investigates a production inventory model under classical EPQ framework with the assumption that the customer demand during the stock out period is affected by the accumulated back-orders. The backlog rate is not fixed; instead, the demand rate during stock-out is assumed to decrease proportionally to the existing backlog which is thereby approximated by a piecewise constant function. Deteriorating items are taken into consideration in this proposed work. For better illustration of the theoretical results and to highlight managerial insights, numerical examples arepresentedwhicharethencomparedtotheresultsobtainedbyconsideringanexact (non-approximated) backlogging rate (from literature). The comparisons indicate high quality results for the approximated model.

Lp-Theory for the fractional time stochastic heat equation with an infinite-dimensional fractional Brownian motion

2021 ◽  
Vol 24 (02) ◽  
pp. 2150010
Author(s):  
Jingqi Han ◽  
Litan Yan
Keyword(s):  
Brownian Motion ◽  
Heat Equation ◽  
Fractional Brownian Motion ◽  
Stochastic Heat Equation ◽  
Index Formula ◽  
Hurst Index ◽  
Skorohod Integral ◽  
Fractional Brownian Motions ◽  
Infinite Dimensional ◽  
Lp Theory

In this paper, we study the [Formula: see text]-theory of the fractional time stochastic heat equation [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] denotes the Caputo derivative of order [Formula: see text], and [Formula: see text] is a sequence of i.i.d. fractional Brownian motions with a same Hurst index [Formula: see text]. The integral with respect to fractional Brownian motion is the Skorohod integral. By using the Malliavin calculus techniques and fractional calculus, we obtain a generalized Littlewood–Paley inequality, and prove the existence and uniqueness of [Formula: see text]-solution to such equation.

Sign in / Sign up

Export Citation Format

Share Document