Related papers: Prediction
We consider the stochastic volatility model obtained by adding a compound Hawkes process to the volatility of the well-known Heston model. A Hawkes process is a self-exciting counting process with many applications in mathematical finance,…
Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable…
Earthquakes are a major threat to nations worldwide. Earthquake detection is an important scientific challenge, not only for its social impacts, but also since it reflects the actual degree of understanding of the physical processes…
This two-part paper presents a new approach to predictive analysis for social processes. In Part I, we begin by identifying a class of social processes which are simultaneously important in applications and difficult to predict using…
Many natural phenomena evolve intermittently, with periods of tranquillity interrupted by bursts of activity, rather than following a smooth gradual path. Examples include earthquakes, volcanic eruptions, solar flares, gamma-ray bursts, and…
There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
The Hawkes process has become a standard method for modeling self-exciting event sequences with different event types. A recent work has generalized the Hawkes process to a neurally self-modulating multivariate point process, which enables…
Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
The methods of the probability theory have been used in order to build up a new model of hysteresis. It turns out that the reversal points of the control parameter (e. g., the magnetic field) are Markov points which determine the stochastic…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
Induced seismicity has emerged as a source of a significant earthquake hazard associated with recent development of unconventional energy resources. Therefore, it is imperative to develop stochastic models that can accurately describe the…
A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a…
The methods of statistical physics of open systems are used for describing the time dependence of economic characteristics (income, profit, cost, supply, currency etc.) and their correlations with each other. Nonlinear equations (analogies…
Interictal spikes and sharp waves in human EEG are characteristic signatures of epilepsy. These potentials originate as a result of synchronous, pathological discharge of many neurons. The reliable detection of such potentials has been the…
Cascading chains of events are a salient feature of many real-world social, biological, and financial networks. In social networks, social reciprocity accounts for retaliations in gang interactions, proxy wars in nation-state conflicts, or…