Related papers: The tail process revisited
A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the {\it Law of Self-Similar Evolution}, according to which any complex system develops self-similarly.…
There is given a method for estimation of a probability distribution tail in terms of characteristic function. Key words: characteristic function; tail of a distribution.
We extend Goldie's implicit renewal theorem to the arithmetic case, which allows us to determine the tail behavior of the solution of various random fixed point equations. It turns out that the arithmetic and nonarithmetic cases are very…
The long-time behavior of the velocity autocorrelation function in a classical two-dimensional electric conduction system is studied by the molecular dynamics simulation. In equilibrium, the effect of coexistence of many-body interactions…
A Lindley process arises from classical studies in queueing theory and it usually reflects waiting times of customers in single server models. In this note we study recurrence of its higher dimensional counterpart under some mild…
This paper studies properties of functions having monotone tails. We extend Theorem 1 of Dhaene et al. (2002a) and show how the tail quantiles of a random variable transformed with a monotone tail function can be expressed as the…
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…
We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with…
Measurement in biological systems became a subject of concern as a consequence of numerous reports on limited reproducibility of experimental results. To reveal origins of this inconsistency, we have examined general features of biological…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
The class of locally stationary processes assumes that there is a time-varying spectral representation, that is, the existence of finite second moment. We propose the $\alpha$-stable locally stationary process by modifying the innovations…
Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. Despite their relevance, a general mathematical…
For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of…
For a class of one-dimensional autoregressive processes $(X_n)$ we consider the tail behaviour of the stopping time $T_0=\min \lbrace n\geq 1: X_n\leq 0 \rbrace$. We discuss existing general analytical approaches to this and related…
Many psychological experiments have subjects repeat a task to gain the statistical precision required to test quantitative theories of psychological performance. In such experiments, time-on-task can have sizable effects on performance,…
Since the turn of the century, there has been increased interest in the application of heavy-tailed distributions, particularly stable distributions, to problems in physics and finance. Although, the tails of stable distributions provide a…
For multitype branching processes with immigration evolving in a random environment and producing a final product we find the tail distribution of the size of the final product accumulated in the system for a life period. Using this result…
Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as…
We present a differentially private mechanism to display statistics (e.g., the moving average) of a stream of real valued observations where the bound on each observation is either too conservative or unknown in advance. This is…
The usual formulation of Macrorealism is recast to make this notion fully concurrent with the basic ideas behind classical physics. The assumption of non-invasiveness of measurements is dropped. Instead, it is assumed that the current state…