In this paper, we present a comprehensive survey of continuous stochastic volatility models,
discussing their historical development and the key stylized facts that have driven the field …

This study proposes a general parameter estimation neural network (PENN) to jointly
identify the system parameters and the noise parameters of a stochastic differential equation …

This work proposes a data-driven parameter identification approach for a two-degree-of-
freedom airfoil system with cubic nonlinearity and stochasticity, where the random turbulent …

We present a method to infer the arbitrary space-dependent drift and diffusion of a nonlinear
stochastic model driven by multiplicative fractional Gaussian noise from a single trajectory …

Stochastic Analysis of Mixed Fractional Gaussian Processes presents the main tools
necessary to characterize Gaussian processes. The book focuses on the particular case of …

This paper estimates the drift parameters in the fractional Vasicek model from a continuous
record of observations via maximum likelihood (ML). The asymptotic theory for the ML …

I survey and illustrate the main time series models that Mandelbrot introduced into time
series analysis in the 1960s and 1970s. I focus particularly on the members of the additive …

We study a class of fractional stochastic differential equations (FSDEs) with coefficients that
may not satisfy the linear growth condition and non-Lipschitz diffusion coefficient. Using the …

Abstract [eng] Strongly consistent and asymptotically normal estimate of the Hurst index H
are obtained for stochastic differential equations (SDEs) that have a unique positive solution …

Let us consider a stochastic differential equation driven by a fractional Brownian motion with
Hurst parameter 1/4< H< 1/2 1/4< H< 1/2. We are interested in estimating the drift parameter …