[图书][B] Stochastic calculus for fractional Brownian motion and related processes

Y Mishura - 2008 - books.google.com
This volume examines the theory of fractional Brownian motion and other long-memory
processes. Interesting topics for PhD students and specialists in probability theory …

Stein's method on Wiener chaos

I Nourdin, G Peccati - Probability Theory and Related Fields, 2009 - Springer
We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the
Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a …

Simulation and inference for stochastic processes with YUIMA

SM Iacus, N Yoshida - A comprehensive R framework for SDEs and other …, 2018 - Springer
Statistics for stochastic processes is rapidly developing. It forms a branch of mathematical
sciences, spreading over theoretical statistics, probability theory, software development and …

Central and non-central limit theorems for weighted power variations of fractional Brownian motion

I Nourdin, D Nualart, CA Tudor - Annales de l'IHP Probabilités et …, 2010 - numdam.org
Central and non-central limit theorems for weighted power variations of fractional Brownian
motion Page 1 www.imstat.org/aihp Annales de l’Institut Henri Poincaré - Probabilités et …

The pathwise convergence of approximation schemes for stochastic differential equations

PE Kloeden, A Neuenkirch - LMS journal of Computation and …, 2007 - cambridge.org
The authors of this paper study approximation methods for stochastic differential equations,
and point out a simple relation between the order of convergence in the pth mean and the …

A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion

A Deya, A Neuenkirch, S Tindel - Annales de l'IHP Probabilités et …, 2012 - numdam.org
In this article, we study the numerical approximation of stochastic differential equations
driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater …

Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions

Y Hu, Y Liu, D Nualart - 2016 - projecteuclid.org
For a stochastic differential equation (SDE) driven by a fractional Brownian motion (fBm) with
Hurst parameter H>12, it is known that the existing (naive) Euler scheme has the rate of …

Parameter estimation for the discretely observed fractional Ornstein–Uhlenbeck process and the Yuima R package

A Brouste, SM Iacus - Computational Statistics, 2013 - Springer
This paper proposes consistent and asymptotically Gaussian estimators for the parameters
λ, σ and H of the discretely observed fractional Ornstein–Uhlenbeck process solution of the …

Noncentral convergence of multiple integrals

I Nourdin, G Peccati - 2009 - projecteuclid.org
Fix ν> 0, denote by G (ν/2) a Gamma random variable with parameter ν/2 and let n≥ 2 be a
fixed even integer. Consider a sequence {F k} k≥ 1 of square integrable random variables …

Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst Index H > 1/2

YS Mishura, GM Shevchenko - Communications in Statistics …, 2011 - Taylor & Francis
Full article: Existence and Uniqueness of the Solution of Stochastic Differential Equation
Involving Wiener Process and Fractional Brownian Motion with Hurst Index H > 1/2 Skip to Main …