scholarly journals Self-exciting multifractional processes

2021 ◽  
Vol 58 (1) ◽  
pp. 22-41
Author(s):  
Fabian A. Harang ◽  
Marc Lagunas-Merino ◽  
Salvador Ortiz-Latorre
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Rate Of Convergence ◽  
Existence And Uniqueness ◽  
Volterra Equation ◽  
The Self ◽  
The Past ◽  
Stochastic Volterra Equation ◽  
Multifractional Brownian Motion ◽  
Self Organizing

AbstractWe propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this by means of a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as giving bounds on the p-order moments, for all $p\geq1$. We show convergence of an Euler–Maruyama scheme for the process, and also give the rate of convergence, which is dependent on the self-exciting dynamics of the process. Moreover, we discuss various applications of this process, and give examples of different functions to model self-exciting behavior.

scholarly journals Stochastic Volterra Equation Driven by Wiener Process and Fractional Brownian Motion

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Zhi Wang ◽  
Litan Yan
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Wiener Process ◽  
Existence And Uniqueness ◽  
Volterra Equation ◽  
Uniqueness Result ◽  
Hurst Parameter ◽  
Stochastic Volterra Equation

For a mixed stochastic Volterra equation driven by Wiener process and fractional Brownian motion with Hurst parameterH>1/2, we prove an existence and uniqueness result for this equation under suitable assumptions.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Self-intersection local times for multifractional Brownian motion in higher dimensions: A white noise approach

2020 ◽  
Vol 23 (01) ◽  
pp. 2050007
Author(s):  
Wolfgang Bock ◽  
Jose Luis da Silva ◽  
Herry Pribawanto Suryawan
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Noise Analysis ◽  
Higher Dimensions ◽  
Kernel Functions ◽  
The Self ◽  
Local Times ◽  
Multifractional Brownian Motion ◽  
White Noises ◽  
Intersection Local Times

In this paper, we study the self-intersection local times of multifractional Brownian motion (mBm) in higher dimensions in the framework of white noise analysis. We show that when a suitable number of kernel functions of self-intersection local times of mBm are truncated then we obtain a Hida distribution. In addition, we present the expansion of the self-intersection local times in terms of Wick powers of white noises. Moreover, we obtain the convergence of the regularized truncated self-intersection local times in the sense of Hida distributions.

Deplay BSDEs driven by fractional Brownian motion

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Sadibou Aidara ◽  
Ibrahima Sane
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Existence And Uniqueness ◽  
Stochastic Integral ◽  
Hurst Parameter ◽  
The Past ◽  
Type Integral ◽  
Divergence Type ◽  
Uniqueness Of A Solution

Abstract This paper deals with a class of deplay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1 2 {\frac{1}{2}} ). In this type of equation, a generator at time t can depend not only on the present but also the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout this paper is the divergence-type integral.

scholarly journals Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

scholarly journals Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (2) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

scholarly journals An Intelligent Evaluation Method to Analyze the Competitiveness of Airlines

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Jun Zhao ◽  
Xumei Chen
Keyword(s):  
Neural Network ◽  
Prior Knowledge ◽  
Evaluation Method ◽  
Standard Sample ◽  
Reference Value ◽  
The Self ◽  
Index Data ◽  
Som Neural Network ◽  
Simulation Results ◽  
Self Organizing

An intelligent evaluation method is presented to analyze the competitiveness of airlines. From the perspective of safety, service, and normality, we establish the competitiveness indexes of traffic rights and the standard sample base. The self-organizing mapping (SOM) neural network is utilized to self-organize and self-learn the samples in the state of no supervision and prior knowledge. The training steps of high convergence speed and high clustering accuracy are determined based on the multistep setting. The typical airlines index data are utilized to verify the effect of the self-organizing mapping neural network on the airline competitiveness analysis. The simulation results show that the self-organizing mapping neural network can accurately and effectively classify and evaluate the competitiveness of airlines, and the results have important reference value for the allocation of traffic rights resources.

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