12,500 research outputs found
Multivariate type G Mat\'ern stochastic partial differential equation random fields
For many applications with multivariate data, random field models capturing
departures from Gaussianity within realisations are appropriate. For this
reason, we formulate a new class of multivariate non-Gaussian models based on
systems of stochastic partial differential equations with additive type G noise
whose marginal covariance functions are of Mat\'ern type. We consider four
increasingly flexible constructions of the noise, where the first two are
similar to existing copula-based models. In contrast to these, the latter two
constructions can model non-Gaussian spatial data without replicates.
Computationally efficient methods for likelihood-based parameter estimation and
probabilistic prediction are proposed, and the flexibility of the suggested
models is illustrated by numerical examples and two statistical applications
Optimal approximation of anticipating SDEs
In this article, we analyse the optimal approximation of anticipating
stochastic differential equations, where the integral is interpreted in
Skorohod sense. We derive optimal rate of convergence for the mean squared
error at the terminal point and an asymptotically optimal scheme for a class of
linear anticipating SDEs. Although alternative proof techniques are needed, our
results can be seen as generalizations of the corresponding results for It\=o
SDEs. As a key tool we carry over optimal approximation from vectors of
correlated Wiener integrals to a general class of random vectors, which cover
the solutions of the Skorohod SDEs
Nonparametric model reconstruction for stochastic differential equation from discretely observed time-series data
A scheme is developed for estimating state-dependent drift and diffusion
coefficients in a stochastic differential equation from time-series data. The
scheme does not require to specify parametric forms for the drift and diffusion
coefficients in advance. In order to perform the nonparametric estimation, a
maximum likelihood method is combined with a concept based on a kernel density
estimation. In order to deal with discrete observation or sparsity of the
time-series data, a local linearization method is employed, which enables a
fast estimation.Comment: 10 pages, 4 figure
A constructive and unifying framework for zero-bit watermarking
In the watermark detection scenario, also known as zero-bit watermarking, a
watermark, carrying no hidden message, is inserted in content. The watermark
detector checks for the presence of this particular weak signal in content. The
article looks at this problem from a classical detection theory point of view,
but with side information enabled at the embedding side. This means that the
watermark signal is a function of the host content. Our study is twofold. The
first step is to design the best embedding function for a given detection
function, and the best detection function for a given embedding function. This
yields two conditions, which are mixed into one `fundamental' partial
differential equation. It appears that many famous watermarking schemes are
indeed solution to this `fundamental' equation. This study thus gives birth to
a constructive framework unifying solutions, so far perceived as very
different.Comment: submitted to IEEE Trans. on Information Forensics and Securit
- …