# On high-order discrete derivatives of stochastic variables

@article{Moriya2006OnHD, title={On high-order discrete derivatives of stochastic variables}, author={N. Moriya}, journal={Applied Mathematical Modelling}, year={2006}, volume={30}, pages={816-823} }

We derive an explicit expression for the probability density function of the mth numerical derivative of a stochastic variable. It is shown that the proposed statistics can analytically be obtained based on the original probability characteristics of the observed signal in a simple manner. We argue that this allows estimating the statistical parameters of the original distribution and further, to simulate the noise contribution in the original stochastic process so that the noise component is… Expand

#### 3 Citations

Noise-level determination for discrete spectra with Gaussian or Lorentzian probability density functions

- Physics
- 2010

A method, based on binomial filtering, to estimate the noise level of an arbitrary, smoothed pure signal, contaminated with an additive, uncorrelated noise component is presented. If the noise… Expand

NON-STATIONARY NOISE ESTIMATION IN ADAPTIVE LINEAR AND EXTENDED KALMAN FILTERING

- 2007

Abstract. When Optimal Linear Kalman Filtering is employed, the complete knowledge of all system parameters, including the forcing input functions and the noise statistics, is required. In Adaptive… Expand

Frequency Estimation From Limited Samples: Nonlinearizing Time-of-Flight Radial Velocity Estimation

- Mathematics
- IEEE Sensors Letters
- 2020

Radial motion in indirect time-of-flight range imaging causes instantaneous frequency shifts in the data. Instantaneous frequency estimation is a well studied topic, but existing methods are either… Expand

#### References

SHOWING 1-10 OF 24 REFERENCES

The generation of diffusion Markovian processes with probability density function defined on part of the real axis

- Computer Science, Mathematics
- IEEE Signal Processing Letters
- 1996

The approach presented provides excellent results in modeling significant non-Gaussian processes with approximately an exponential correlation function and is validated by direct numerical simulation of a uniformly distributed correlated process. Expand

Model-based probability density function estimation

- Computer Science, Mathematics
- IEEE Signal Processing Letters
- 1998

A new class of probability density function estimators is described, based on the autoregressive model, which has similar properties to a power spectral density of a continuous random variable. Expand

Estimation of noise levels for models of chaotic dynamical systems

- Mathematics, Medicine
- Physical review letters
- 2000

Using Bayesian methods, estimates for the two noise levels are derived and it is argued that this allows better estimates of the underlying dynamical time series, and so better predictions of its future and of its fundamental dynamical properties. Expand

Computing the bivariate Gaussian probability integral

- Mathematics, Computer Science
- IEEE Signal Processing Letters
- 1999

The closed form solution to the integral of the bivariate Gaussian probability density function over the four quadrants is derived using the characteristic function method in terms of the well-known confluent hypergeometric function. Expand

Supersymmetry in stochastic processes with higher-order time derivatives

- Physics
- 1997

Abstract A supersymmetric path-integral representation is developed for stochastic processes whose Langevin equation contains any number N of time derivatives, thus generalizing the presently… Expand

Estimation based on entropy matching for generalized Gaussian PDF modeling

- Mathematics, Computer Science
- IEEE Signal Processing Letters
- 1999

A novel method for estimating the shape factor of a generalized Gaussian probability density function that relies on matching the entropy of the modeled distribution with that of the empirical data is presented and assessed. Expand

General exact solution to the problem of the probability density for sums of random variables.

- Medicine, Physics
- Physical review letters
- 2002

The exact explicit expression for the probability density p(N)(x) for a sum of N random, arbitrary correlated summands is obtained and it is shown that if the distribution is not stable, the profile is divided into three parts, namely a core, a tail, and a crossover from the core to the tail. Expand

Stochastic Analysis and Random Maps in Hilbert Space

- Mathematics
- 1994

Part 1 Stochastic calculus: preliminaries (L2-theory) smooth open sets the localization of the extended stochastic integral and the stochastic derivative stochastic integrals with respect to Gaussian… Expand

APPL

- 2001

Statistical packages have been used for decades to analyze large datasets or to perform mathematically intractable statistical methods. These packages are not capable of working with random variables… Expand

Quantum chaotic environments, the butterfly effect, and decoherence.

- Physics, Medicine
- Physical review letters
- 2002

This work investigates the sensitivity of quantum systems that are chaotic in a classical limit to small perturbations of their equations of motion to find out whether this sensitivity is relevant to decoherence when the environment has a chaotic classical counterpart. Expand