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After the main shock of an earthquake the aftershocks are observed. According to Omori's law, the frequency of aftershocks decreases hyperbolically over time. We noticed that, strictly speaking, Omori's law paradoxically contradicts the law…
After the main shock of an earthquake, a stream of aftershocks that does not subside for a long time is usually observed. Fusakichi Omori found that the frequency of aftershocks decreases hyperbolically with time. It has recently been…
The decay rate of aftershocks is commonly very well described by the modified Omori law, $n(t) \propto t^{-p}$, where n(t) is the number of aftershocks per unit time, t is the time after the main shock, and p is a constant in the range…
The paper is based on the report read by the author on October 24, 2018 at the meeting of the Scientific Council of the Institute of Earth Physics of the Russian Academy of Sciences. The report was dedicated to the 150th anniversary of the…
We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich [1994].We show that an exponential stress distribution Pt(au) ~exp(-tautau_0) gives an Omori law decay of…
In this study we examine the evolution of price, volume, and the bid-ask spread after extreme 15 minute intraday price changes on the NYSE and the NASDAQ. We find that due to strong behavioral trading there is an overreaction. Furthermore…
We study how a stress perturbation generated by a mainshock affects a population of faults obeying a rate-state friction law. Depending on the model parameters and on the initial state, the fault exhibits aftershocks, slow earthquakes, or…
In this empirical paper we show that in the months following a crash there is a distinct connection between the fall of stock prices and the increase in the range of interest rates for a sample of bonds. This variable, which is often…
We present an analytical solution and numerical tests of the epidemic-type aftershock (ETAS) model for aftershocks, which describes foreshocks, aftershocks and mainshocks on the same footing. The occurrence rate of aftershocks triggered by…
The decay pattern of aftershocks in the so-called 'coherent-noise' models [M. E. J. Newman and K. Sneppen, Phys. Rev. E54, 6226 (1996)] is studied in detail. Analytical and numerical results show that the probability to find a large event…
We present a Hawkes model approach to foreign exchange market in which the high frequency price dynamics is affected by a self exciting mechanism and an exogenous component, generated by the pre-announced arrival of macroeconomic news. By…
We find the static displacement, stress, strain and the modified Columb failure stress produced in an elastic medium by a finite size rectangular fault after its dislocation with uniform stress drop but a non uniform dislocation on the…
Omori Law describes the evolution of the aftershocks of a strong earthquake. Established at the end of the century before last, it is characterized by the beauty of its form, quite definite clarity, as a result of which it still attracts…
This paper examines how regulatory interventions in high-frequency financial markets affect price discovery. We focus on Breaking news, where dynamic circuit breakers trigger trading halts immediately after the release of macroeconomic…
The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary…
The acoustic emission activity associated with recent rock fracture experiments under different conditions has indicated that some features of event-event triggering are independent of the details of the experiment and the materials used…
We consider two statistical regularities that were used to explain Omori's law of the aftershock rate decay: the Levy and Inverse Gaussian (IGD) distributions. These distributions are thought to describe stress behavior influenced by…
We propose a simple theory for the ``universal'' scaling law previously reported for the distributions of waiting times between earthquakes. It is based on a largely used benchmark model of seismicity, which just assumes no difference in…
The statistical properties of earthquake aftershocks are studied. The scaling relation for the exponents of the Omori law and the power-law calm time distribution (i.e., the interoccurrence time distribution), which is valid if a sequence…
Earthquakes are complex physical processes driven by the stick-slip motion of a sliding fault. After the main quake, a series of aftershocks typically follows. These are loosely defined as events that follow a given event and occur within…