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The Integral Fluctuation Theorem for entropy production (IFT) is among the few equalities that are known to be valid for physical systems arbitrarily driven far from equilibrium. Microscopically, it can be understood as an inherent symmetry…

Statistical Mechanics · Physics 2023-06-21 Francesco Coghi , Lorenzo Buffoni , Stefano Gherardini

We consider a longitudinal data structure consisting of baseline covariates, time-varying treatment variables, intermediate time-dependent covariates, and a possibly time dependent outcome. Previous studies have shown that estimating the…

Statistics Theory · Mathematics 2018-10-09 Linh Tran , Maya Petersen , Joshua Schwab , Mark J van der Laan

We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators' properties. These estimators are applicable despite the presence of Brownian volatility in the…

Statistics Theory · Mathematics 2009-08-24 Yacine Aït-Sahalia , Jean Jacod

In this paper we consider a fractional stochastic volatility model, that is a model in which the volatility may exhibit a long-range dependent or a rough/antipersistent behavior. We propose a dynamic sequential Monte Carlo methodology that…

Methodology · Statistics 2017-02-28 Alexandra Chronopoulou , Konstantinos Spiliopoulos

We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…

Statistical Mechanics · Physics 2021-01-14 Avishek Das , David T. Limmer

Consider the sum $Y=B+B(H)$ of a Brownian motion $B$ and an independent fractional Brownian motion $B(H)$ with Hurst parameter $H\in(0,1)$. Even though $B(H)$ is not a semimartingale, it was shown in [\textit{Bernoulli} \textbf{7} (2001)…

Statistics Theory · Mathematics 2024-10-28 Carsten H. Chong , Thomas Delerue , Fabian Mies

We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter $H$ of the fractional part…

Probability · Mathematics 2015-06-08 Ehsan Azmoodeh , Tommi Sottinen , Lauri Viitasaari

We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…

Statistics Theory · Mathematics 2014-07-02 Jean-François Coeurjolly , Jesper Møller

Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation.…

Computational Finance · Quantitative Finance 2010-06-17 Don McLeish

We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling…

Probability · Mathematics 2008-12-02 Erhan Bayraktar , Ulrich Horst , Ronnie Sircar

We consider statistical inference for a class of continuous semimartingale regression models based on high-frequency observations subject to contamination by finite-activity jumps and spike noise. By employing density-power weighting and…

Statistics Theory · Mathematics 2026-01-01 Shoichi Eguchi , Hiroki Masuda

This article presents various weak laws of large numbers for the so-called realised covariation of a bivariate stationary stochastic process which is not a semimartingale. More precisely, we consider two cases: Bivariate moving average…

Probability · Mathematics 2017-07-27 Andrea Granelli , Almut E. D. Veraart

Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…

Machine Learning · Computer Science 2022-03-22 Nhat Ho , Koulik Khamaru , Raaz Dwivedi , Martin J. Wainwright , Michael I. Jordan , Bin Yu

We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma…

Statistics Theory · Mathematics 2023-10-18 Denis Belomestny , Shota Gugushvili , Moritz Schauer , Peter Spreij

Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised.…

Statistical Finance · Quantitative Finance 2016-10-11 F Blasques , P Gorgi , S Koopman , O Wintenberger

We show that if a random variable is a final value of an adapted Holder continuous process, then it can be represented as a stochastic integral with respect to fractional Brownian motion, and the integrand is an adapted process, continuous…

Probability · Mathematics 2014-03-11 Georgiy Shevchenko , Lauri Viitasaari

In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the…

Information Theory · Computer Science 2007-07-13 Erhan Bayraktar , H. Vincent Poor

A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…

Statistics Theory · Mathematics 2017-02-06 Alberto J. Coca

Fractional Brownian motion (fBm) is a canonical model for long-memory phenomena. In the presence of large amounts of potentially memory-bearing data, the data are often averaged, which can change the structure of the underlying…

In this note we consider the finite-dimensional parameter estimation problem associated to inverse problems. In such scenarios, one seeks to maximize the marginal likelihood associated to a Bayesian model. This latter model is connected to…

Numerical Analysis · Mathematics 2025-04-10 Ajay Jasra , Abylay Zhumekenov