Some results for the quadratic analysis of Gaussian processes and applications
Some results on stochastic convolutions arising in Volterra equations perturbed by noise
Regularity of stochastic convolutions corresponding to a Volterra equation, perturbed by a white noise, is studied. Under suitable assumptions, hölderianity of the corresponding trajectories is proved.
Some Results On Subexponential Distributions
Some results on summability of random variables.
Some results on the continuity of stable processes and the domain of attraction of continuous stable processes
Some results on the influence of extremes on the bootstrap
Some Sawyer type inequalities for martingales
Some martingale analogues of Sawyer's two-weight norm inequality for the Hardy-Littlewood maximal function Mf are shown for the Doob maximal function of martingales.
Some Shannon-McMillan approximation theorems for Markov chain field on the generalized Bethe tree.
Some thoughts about Segal's ergodic theorem
Over fifty years ago, Irving Segal proved a theorem which leads to a characterization of those orthogonal transformations on a Hilbert space which induce ergodic transformations. Because Segal did not present his result in a way which made it readily accessible to specialists in ergodic theory, it was difficult for them to appreciate what he had done. The purpose of this note is to state and prove Segal's result in a way which, I hope, will win it the recognition which it deserves.
Some universal field equations
Some use of some “symmetries” of some random process
Sous-espaces denses dans ou et représentation des martingales
Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction
We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory...
Spatial structure analysis using planar indices.
Spatial planar indices have become a useful tool to analyze patterns of points. Despite that, no simulation study has been reported in literature in order to analyze the behaviour of these quantities under different pattern structures. We present here an extensive Monte Carlo simulation study focused on two important indices: the Index of Dispersion and the Index of Cluster Size, usually used to detect lack of homogeneity in a spatial point model. Finally, an application is also presented.
Spatial trajectories
Spatio-temporal modelling of a Cox point process sampled by a curve, filtering and Inference
The paper deals with Cox point processes in time and space with Lévy based driving intensity. Using the generating functional, formulas for theoretical characteristics are available. Because of potential applications in biology a Cox process sampled by a curve is discussed in detail. The filtering of the driving intensity based on observed point process events is developed in space and time for a parametric model with a background driving compound Poisson field delimited by special test sets. A...
Special, conjugate and complete scale functions for spectrally negative Lev́y processes.
Spectral analysis of subordinate Brownian motions on the half-line
We study one-dimensional Lévy processes with Lévy-Khintchine exponent ψ(ξ²), where ψ is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators whose Lévy measure has completely monotone density; or, equivalently, symmetric Lévy processes whose Lévy measure has completely monotone density on (0,∞). Examples include symmetric stable processes and relativistic processes. The main result is a formula for the generalized eigenfunctions of transition...
Spectral approach for kernel-based interpolation
We describe how the resolution of a kernel-based interpolation problem can be associated with a spectral problem. An integral operator is defined from the embedding of the considered Hilbert subspace into an auxiliary Hilbert space of square-integrable functions. We finally obtain a spectral representation of the interpolating elements which allows their approximation by spectral truncation. As an illustration, we show how this approach can be used to enforce boundary conditions in kernel-based...
Spectral approximation of infinite-dimensional Black-Scholes equations with memory.