Abstract: Let {Xn, n=1} be a sequences of i.i.d. random variables with survival function 1 F(x) P[X x] = > . A wavelet linear survival function n F(x) based on X1, X2,..., Xn is introduced as an estimator for n F(x) . We establish that the Lp’-loss (2=r=p′= ∞) of the linear wavelet survival function estimator for a stochastic processes convergence at the rate rs 2 s 1 n (s s 1 /p 1 / p ) ′ − ′+...

It is shown that if (Xn)n is a Bochner integrable stochastic process taking values in a Banach lattice E, the convergence of f(Xn) to f(X) where f is in a total subset of E∗ implies the a.s. convergence. For any Banach space E-valued stochastic process of Pettis integrable strongly measurable functions (Xn)n, the convergence of f(Xn) to f(X) for each f in a total subset of E∗ implies the conver...

In a noncommutative torus, effect of perturbation by inner derivation on the associated quantum stochastic process and geometric parameters like volume and scalar curvature have been studied. Cohomological calculations show that the above perturbation produces new spectral triples. Also for the Weyl C-algebra, the Laplacian associated with a natural stochastic process is obtained and associated...

We describe an extension of Gaussian interest rate models studied in literature. In our model, the instantaneous spot rate r is the sum of several correlated stochastic processes plus a deterministic function. We assume that each of these processes has a Gaussian distribution with time-dependent volatility. The deterministic function is given by an exact fitting to observed term structure. We t...

A stochastic process of long-term evolution due to mutation and selection is defined over an asexually reproducing population, with selection according to a population game with a one-dimensional continuity of pure strategies. Limiting the analysis to mutations of small effect, it is shown that long-term dynamic stability in such a process is equivalent to continuous stability in the relevant p...

We assess the predictive capabilities of various classes of avalanche models for solar flares. We demonstrate that avalanche models cannot generally be used to predict specific events due to their high sensitivity to their embedded stochastic process. We show that deterministically driven models can nevertheless alleviate this caveat and be efficiently used for large events predictions. Our res...

We propose a new methodology for the analysis of impulse response functions in VAR or VARMA models. More precisely, we build our results on the non ambiguous notion of innovation of a stochastic process and we consider the impact of any kind of new information at a given date t on the future values of the process. This methodology allows to take into account qualitative or quantitative informat...

We introduce a new framework for constructing tests of a general semiparametric hypotheses which (i) have non-trivial power on the n−1/2 scale in every direction. (ii) can be tailored to put substantial power on alternatives of importance. The approach is based on combining test statistics based on stochastic processes of score statistics with bootstrap critical values.

Abstract. The periodic Lorentz gas describes an ensemble of non-interacting point particles in a periodic array of spherical scatterers. We have recently shown that, in the limit of small scatterer density (Boltzmann-Grad limit), the macroscopic dynamics converges to a stochastic process, whose kinetic transport equation is not the linear Boltzmann equation—in contrast to the Lorentz gas with a...

This methodological paper proposes a new class of stochastic processes with appealing properties for theoretical or empirical work in finance and macroeconomics, the “linearity-inducing” class. Its key property is that it yields simple exact closed-form expressions for stocks and bonds, with an arbitrary number of factors, feats that are not possible with the hitherto available modelling method...