Fractionally integrated Bessel process
Анотація
We consider a fractionally integrated Bessel process defined by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Y</mml:mi> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>H</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mo>∫</mml:mo> <mml:mn>0</mml:mn> <mml:mi mathvariant="normal">∞</mml:mi> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mi>u</mml:mi> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>−</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>u</mml:mi> <mml:mo>−</mml:mo> <mml:mi>s</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>−</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mtext>d</mml:mtext> </mml:mrow> <mml:msubsup> <mml:mi>X</mml:mi> <mml:mi>u</mml:mi> <mml:mi>δ</mml:mi> </mml:msubsup> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>X</mml:mi> <mml:mi>δ</mml:mi> </mml:msup> </mml:math> is the Bessel process of dimension δ > 2. We discuss the relation of this process to the fractional Brownian motion at its maximum, study the basic properties of the process and prove its Hölder continuity.
Класифікація
Ідентифікатори
Рецензії (0)
Написати рецензіюРецензій ще немає. Будьте першим!
Схожі роботи
Properties of trajectories of a multifractional Rosenblatt process
Схоже за: Stochastic processes and financial applications · Fractional Differential Equations Solutions · Nonlinear Differential Equations Analysis
Fractional Diffusion Bessel Processes with Hurst Index [[Equation]]
Схоже за: Stochastic processes and financial applications · Fractional Differential Equations Solutions · Nonlinear Differential Equations Analysis
Drift Parameter Estimation in Diffusion and Fractional Diffusion Models
Схоже за: Stochastic processes and financial applications · Fractional Differential Equations Solutions
Strong uniqueness of solutions of stochastic differential equations with jumps and non-Lipschitz random coefficients
Схоже за: Stochastic processes and financial applications · Nonlinear Differential Equations Analysis
Existence and Uniqueness of Solution of Stochastic Dynamic Systems with Markov Switching and Concentration Points
Схоже за: Stochastic processes and financial applications · Nonlinear Differential Equations Analysis
Approximation of solutions of stochastic differential equations with fractional Brownian motion by solutions of random ordinary differential equations
Схоже за: Stochastic processes and financial applications · Nonlinear Differential Equations Analysis