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We present a general numerical scheme for the practical implementation of statistical moment closures suitable for modeling complex, large-scale, nonlinear systems. Building on recently developed equation-free methods, this approach…
For tridiagonal block Jacobi operators, the standard transfer operator techniques only work if the off-diagonal entries are invertible. Under suitable assumptions on the range and kernel of these off-diagonal operators which assure a…
Solving inverse scattering problem for a discrete Sturm-Liouville operator with the fast decreasing potential one gets reflection coefficients $s_\pm$ and invertible operators $I+H_{s_\pm}$, where $ H_{s_\pm}$ is the Hankel operator related…
Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…
In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…
Infinite horizon optimal stopping problems for a L\'evy processes with a two-sided reward function are considered. A two-sided verification theorem is presented in terms of the overall supremum and the overall infimum of the process. A…
Offline Reinforcement learning is commonly used for sequential decision-making in domains such as healthcare and education, where the rewards are known and the transition dynamics $T$ must be estimated on the basis of batch data. A key…
We prove fourteen equivalent conditions for a set of timefrequency shifts on a lattice to be a frame for L^2. Remarkably, several of these conditions can be formulated without an inequality. In particular, instead of checking the…
Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme…
In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase transition are introduced and…
[abridged] Inversion techniques are the most powerful methods to obtain information about the thermodynamical and magnetic properties of solar and stellar atmospheres. In the last years, we have witnessed the development of highly…
In this article, the problem of semi-parametric inference on the parameters of a multidimensional L\'{e}vy process $L_t$ with independent components based on the low-frequency observations of the corresponding time-changed L\'{e}vy process…
The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective…
The term noncentral moderate deviations is used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between the convergence in probability to a constant (governed by a reference large deviation…
We discuss conditions under which expectation values computed from a complex Langevin process $Z$ will converge to integral averages over a given complex valued weight function. The difficulties in proving a general result are pointed out.…
In this paper, we study weak and strong transience of a class of Feller processes associated with pseudo-differential operators, the so-called L\'evy-type processes. As a main result, we derive Chung-Fuchs type conditions (in terms of the…
The inverse problem associated with electrochemical impedance spectroscopy requiring the solution of a Fredholm integral equation of the first kind is considered. If the underlying physical model is not clearly determined, the inverse…
We develop a general strategy in order to implement (approximate) discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is a rectangle equipped with…
By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $\rho(E)$ for the L\'evy and the L\'evy -Rosenzweig-Porter random matrices which off-diagonal elements are strongly non-Gaussian with…
This article deals with adaptive nonparametric estimation for L\'evy processes observed at low frequency. For general linear functionals of the L\'evy measure, we construct kernel estimators, provide upper risk bounds and derive rates of…