Related papers: Random Processes with Stationary Increments and In…
We address the counting of level crossings for inertial stochastic processes. We review Rice's approach to the problem and generalize the classical Rice formula to include all Gaussian processes in their most general form. We apply the…
We propose solution of the problem of the mean square optimal estimation of linear functionals which depend on the unobserved values of a continuous time stochastic process with periodically correlated increments based on observations of…
Randomness comes in two qualitatively different forms. Apparent randomness can result both from ignorance or lack of control of degrees of freedom in the system. In contrast, intrinsic randomness should not be ascribable to any such cause.…
The opportunity of occurrence of entropy oscillations around of a stationary state in linear and nonlinear processes is theoretically shown. The new mechanism of global tendencies appearance is described.
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation"…
We show that the existence of a martingale approximation of a stationary process depends on the choice of the filtration. There exists a stationary linear process which has a martingale approximation with respect to the natural filtration,…
A new family of stable processes indexed by metric spaces with stationary increments are introduced. They are special cases of a new family of set-indexed stable processes with Chentsov representation. At the heart of the representation, a…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
For a non-stationary or non-ergodic marked point process (MPP) on $\R^d$, the definition of averages becomes ambiguous as the process might have a different stochastic behavior in different realizations (non-ergodicity) or in different…
In the article we study properties of the random integral operator in $L_2(\mathbb{R})$ whose kernel is obtained as a convolution of Gaussian density with a stationary point process.
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…
Stochastic solutions provide new rigorous results for nonlinear PDE's and, through its local non-grid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions:…
We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
We extend Neural Processes (NPs) to sequential data through Recurrent NPs or RNPs, a family of conditional state space models. RNPs model the state space with Neural Processes. Given time series observed on fast real-world time scales but…
We consider several stochastic service systems, and study the asymptotic behavior of the moments of various quantities that have application to models for random interval graphs and algorithms for searching for an idle server or empty…
The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distributions of the time in these states may differ. Two versions of the process are considered: a non-stationary…