Search results for "Stochastic process"
showing 10 items of 346 documents
Segmentation algorithm for non-stationary compound Poisson processes
2010
We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of a time series. The process is composed of consecutive patches of variable length. In each patch the process is described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated with a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non-stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galván, et al. [Phys. Rev. Lett. 87, 168105 (2001)]. We show that the new algori…
Fluctuation patterns in high-frequency financial asset returns
2008
We introduce a new method for quantifying pattern-based complex short-time correlations of a time series. Our correlation measure is 1 for a perfectly correlated and 0 for a random walk time series. When we apply this method to high-frequency time series data of the German DAX future, we find clear correlations on short time scales. In order to subtract trivial autocorrelation parts from the pattern conformity, we introduce a simple model for reproducing the antipersistent regime and use alternatively level 1 quotes. When we remove the pattern conformity of this stochastic process from the original data, remaining pattern-based correlations can be observed.
Internal Time and Innovation
2003
Consider a physical system that may be observed through time-varying quantities x t , where t stands for time that may be discrete or continuous. The set x t may be a realization of a deterministic system, e.g. a unique solution of a differential equation, or a stochastic process. In the latter case each x t is a random variable. We are interested in the global evolution of the system, not particular realizations x t , from the point of view of innovation. We call the evolution innovative if the dynamics of the system is such that there is a gain of information about the system as time increases. Our purpose is to associate the concept of internal time with such systems. The internal time w…
A Simple Noise Model with Memory for Biological Systems
2005
A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory, produces different kinds of correlated noise ranging from white noise, without delay, to quasi-periodical process, with delay close to the average period of the pulses. The spectral density is calculated. This type of noise could be useful to describe physical and biological systems where some delay is present. In particular it could be useful in population dynamics. A simple dynamical model for epidemiological infection with this noise source is presented. We …
Predator population depending on lemming cycles
2016
In this paper, a Langevin equation for predator population with multiplicative correlated noise is analyzed. The noise source, which is a nonnegative random pulse noise with regulated periodicity, corresponds to the prey population cycling. The increase of periodicity of noise affects the average predator density at the stationary state.
Constrained Robust MultiObjective Optimization for Reactive Design in Distribution Systems
2006
This paper presents a new formulation including robustness of solution of constrained multiobjective design or reactive power compensation. The algorithm used for optimization is the NSGA-II (Non dominated Sorting Genetic Algorithm II) with a special crowded comparison operator for constraints handling. The need for including the issue of robustness of solutions derives from the simple observation that loads are uncertain in distribution systems and their estimation is often affected by errors. In design problems it is desirable to consider the loads with a certain range of variation. In this paper the NSGA-II algorithm is applied to efficiently solve the issue and the solutions attained co…
Texture Synthesis for Digital Restoration in the Bit-Plane Representation
2007
In this paper we propose a new approach to handle the problem of restoration of grayscale textured images. The purpose is to recovery missing data of a damaged area. The key point is to decompose an image in its bit-planes, and to process bits rather than pixels. We propose two texture synthesis methods for restoration. The first one is a random generation process, based on the conditional probability of bits in the bit-planes. It is designed for images with stochastic textures. The second one is a best-matching method, running on each bit-plane, that is well suited to synthesize periodic patterns. Results are compared with a state-of-the-art restoration algorithm.
Transfer Entropy Analysis of Pulse Arrival Time - Heart Period Interactions during Physiological Stress
2022
Although Heart Period (HP) variability is the most widely used measure to assess cardiovascular oscillations, its evaluation combined with that of Pulse Arrival Time (PAT) variability may provide additional information about cardiac dynamics and cardiovascular interactions. In this study, we computed the transfer entropy from PAT to HP in 76 subjects monitored at rest and during orthostatic and mental stress using both a model-free (k- Nearest Neighbors) and a linear parametric estimator. Our results show how the information flow between these two variables depends on the physiological condition and how the nonlinear measure captures more information than the linear one during orthostatic s…
Feasibility of Ultra-short Term Complexity Analysis of Heart Rate Variability in Resting State and During Orthostatic Stress
2022
In this work, we study ultra-short term (UST) complexity of Heart Rate Variability (HRV) and its agreement with analysis of standard short-term (ST) HRV recordings obtained at rest and during orthostatic stress. Conditional Entropy (CE) measures have been computed using both a linear Gaussian approximation and a more accurate model-free approach based on nearest neighbors. The agreement between UST and ST indices has been compared via statistical tests and correlation analysis, suggesting the feasibility of exploiting faster algorithms and shorter time series for detecting changes in cardiovascular control during various states.
Analytic evaluation of spectral moments
1988
In this paper an analytic procedure that drastically reduces the computational effort in evaluating the spectral moments of the response of multi-degree-of-freedom systems is presented. It is shown that the cross-spectral moments of any order of two oscillators subjected to a filtered stochastic process can be obtained in a recursive manner as a linear combination of the spectral moment of each oscillator up to the third order separately taken. A numerical procedure is also presented in order to evaluate such first few spectral moments.