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We propose a bivariate model for a pair of dependent unit vectors which is generated by Brownian motion. Both marginals have uniform distributions on the sphere, while the conditionals follow so-called ``exit'' distributions. Some…

Statistics Theory · Mathematics 2009-09-08 Shogo Kato

We discuss maximum likelihood estimation of parameters for models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with random effects.

Probability · Mathematics 2021-05-03 B. L. S. Prakasa Rao

This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…

Probability · Mathematics 2024-10-04 Michael Levine , Xiaoguang Wang , Jian Frank Zou

In this paper, we study small-time asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H\in(1/2,1)$ and magnitude $\ep^H$. By building up a…

Probability · Mathematics 2022-07-05 Xiliang Fan , Ting Yu , Chenggui Yuan

Exact and asymptotic formulas relating to dynamical correlations for overdamped Brownian motion are obtained. These formulas include a generalization of the $f$-sum rule from the theory of quantum fluids, a formula relating the static…

Statistical Mechanics · Physics 2015-06-25 P. J. Forrester , B. Jancovici

We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models.…

Statistics Theory · Mathematics 2015-09-16 Lee H. Dicker , Murat A. Erdogdu

We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation…

Classical Analysis and ODEs · Mathematics 2015-05-07 Adrian Falkowski , Leszek Slominski

We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…

Statistical Finance · Quantitative Finance 2021-01-06 Mikkel Bennedsen , Asger Lunde , Mikko S. Pakkanen

The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a $\gamma$-H\"older continuous process with $\gamma>1/2$ (e.g. a fractional Brownian motion with Hurst parameter greater than…

Probability · Mathematics 2014-07-22 Yuliya Mishura , Taras Shalaiko , Georgiy Shevchenko

We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…

Statistics Theory · Mathematics 2020-12-01 Laura Dumitrescu , Ioana Schiopu-Kratina

We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…

Statistics Theory · Mathematics 2022-05-03 Han Yuecai , Zhang Dingwen

We study the asymptotic behavior of mixed functionals of the form $I_T(t)=F_T(\xi_T(t))+\int_0^tg_T(\xi_T(s))\,d\xi_T(s)$, $t\ge0$, as $T\to\infty$. Here $\xi_T(t)$ is a strong solution of the stochastic differential equation…

Probability · Mathematics 2016-07-14 Grigorij Kulinich , Svitlana Kushnirenko , Yuliia Mishura

We study the asymptotic macroscopic properties of the mixed majority-minority game, modeling a population in which two types of heterogeneous adaptive agents, namely ``fundamentalists'' driven by differentiation and ``trend-followers''…

Statistical Mechanics · Physics 2009-11-10 A. De Martino , I. Giardina , G. Mosetti

Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…

Methodology · Statistics 2024-03-11 Cory W. Natoli , Edward D. White , Beau A. Nunnally , Alex J. Gutman , Raymond R. Hill

We propose a new approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations. Our formalism is based on a nonextensive generalization of the Wiener process. This allow us to obtain, in addition…

Statistical Mechanics · Physics 2021-03-17 Leonardo Santos

We prove absolute regularity ($\beta$-mixing) for nonstationary and multivariate versions of two popular classes of integer-valued processes. We show how this result can be used to prove asymptotic normality of a least squares estimator of…

Statistics Theory · Mathematics 2024-08-29 Zinsou Max Debaly , Michael H. Neumann , Lionel Truquet

The association between two random variables is often of primary interest in statistical research. In this paper semiparametric models for the association between random vectors X and Y are considered which leave the marginal distributions…

Statistics Theory · Mathematics 2012-04-16 Angelika Franke , Gerhard Osius

This paper consider the LAN property for the mixed O-U process under high-frequency observation when H>3/4. As considered in mixed fractional Brownian motion, we will also use the projection step to get the non-diagonal rate matrix.

Statistics Theory · Mathematics 2026-03-18 Chunhao Cai , Yiwu Shang , Cong Zhang

The purpose of this work is to construct a {\it Brownian motion} with values in simplicial complexes with piecewise differential structure. In order to state and prove the existence of such Brownian motion, we define a family of continuous…

Probability · Mathematics 2007-05-23 Taoufik Bouziane

This paper establishes the Local Asymptotic Normality (LAN) property for the mixed fractional Brownian motion under high-frequency observations with Hurst index $H \in (0, 3/4)$. The simultaneous estimation of the volatility and the Hurst…

Statistics Theory · Mathematics 2026-01-01 Chunhao Cai