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We consider a general d-dimensional Levy-type process with killing. Combining the classical Dyson series approach with a novel polynomial expansion of the generator A(t) of the Levy-type process, we derive a family of asymptotic…

Computational Finance · Quantitative Finance 2014-12-01 Matthew Lorig , Stefano Pagliarani , Andrea Pascucci

We estimate a general mixture of Markov jump processes. The key novel feature of the proposed mixture is that the transition intensity matrices of the Markov processes comprising the mixture are entirely unconstrained. The Markov processes…

Methodology · Statistics 2022-04-12 Halina Frydman , Budhi Surya

We prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in…

Statistical Mechanics · Physics 2012-04-06 Takuya Yamano

This paper provides rate-efficient estimators of the volatility parameter in the presence of L\'{e}vy jumps

Statistics Theory · Mathematics 2016-08-16 Yacine Aït-Sahalia , Jean Jacod

We give an online algorithm that keeps a symmetric random walk inside a convex body by discarding some of its steps. The expected number of discarded steps is controlled by a Fisher-information-type quantity associated with the body. For…

Probability · Mathematics 2026-05-14 Gleb Smirnov , Roman Vershynin

For $n$ equidistant observations of a L\'evy process at time distance $\Delta_n$ we consider the problem of testing hypotheses on the volatility, the jump measure and its Blumenthal-Getoor index in a non- or semiparametric manner.…

Statistics Theory · Mathematics 2013-04-05 Markus Reiß

We show that the mathematical form of the information measure of Fisher's I for a Gibbs' canonical probability distribution (the most important one in statistical mechanics) incorporates important features of the intrinsic structure of…

Statistical Mechanics · Physics 2007-05-23 F. Pennini , A. Plastino

Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which…

Quantum Physics · Physics 2012-09-04 Xiao-Ming Lu , Shunlong Luo , C. H. Oh

In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…

Statistics Theory · Mathematics 2008-08-22 Alessandro De Gregorio , Stefano Iacus

Spectroscopy detected in the time domain entails many techniques, such as FTIR, pump-probe, FT-Raman, and 2DES, and applications, such as molecule characterization, excited state dynamics studies, or spectra classifications. Surprisingly,…

Optics · Physics 2024-05-21 Luca Bolzonello , Niek F van Hulst , Andreas Jakobsson

In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central…

Probability · Mathematics 2024-08-20 Nguyen Tien Dung , Nguyen Thu Hang

Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family…

Probability · Mathematics 2019-05-02 Dorje C. Brody , Lane P. Hughston , Xun Yang

We develop data processing inequalities that describe how Fisher information from statistical samples can scale with the privacy parameter $\varepsilon$ under local differential privacy constraints. These bounds are valid under general…

Information Theory · Computer Science 2020-05-22 Leighton Pate Barnes , Wei-Ning Chen , Ayfer Ozgur

An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…

Probability · Mathematics 2012-05-01 S. G. Bobkov , G. P. Chistyakov , F. Götze

Complex frequency excitations, oscillating signals whose amplitude decreases exponentially in time, have recently been demonstrated to significantly increase the effective quality factor of mechanical resonators. In this work, we…

Classical Physics · Physics 2026-05-14 Wenbo Li , Raj Kumar Pal

We study the problem of parameter estimation in time series stemming from general stochastic processes, where the outcomes may exhibit arbitrary temporal correlations. In particular, we address the question of how much Fisher information is…

Statistical Mechanics · Physics 2023-09-06 Joseph A. Smiga , Marco Radaelli , Felix C. Binder , Gabriel T. Landi

In a high-frequency context, we investigate the efficient estimation of scaling and jump activity parameters for a stochastic differential equation driven by a L{\'e}vy process with both diffusion component and pure-jump component. We first…

Probability · Mathematics 2025-09-08 Elise Bayraktar , Emmanuelle Clément

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

Machine Learning · Statistics 2014-02-21 Keisuke Yamazaki

We derive upper bounds on the quantum Fisher information in interferometry with $N$ subsystems, e.g. two-level atoms or Gaussian modes, in the presence of arbitrarily correlated Gaussian dephasing including independent and collective…

Quantum Physics · Physics 2014-03-06 Katarzyna Macieszczak

In this paper we consider two processes driven by diffusions and jumps. The jump components are Levy processes and they can both have finite activity and infinite activity. Given discrete observations we estimate the covariation between the…

Probability · Mathematics 2009-11-13 Fabio Gobbi , Cecilia Mancini