Related papers: Return interval distribution of extreme events and…
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with…
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…
Long range connections play an essential role in dynamical processes on networks, on the processing of information in biological networks, on the structure of social and economical networks and in the propagation of opinions and epidemics.…
We study the extremes of a sequence of random variables $(R_n)$ defined by the recurrence $R_n=M_nR_{n-1}+q$, $n\ge1$, where $R_0$ is arbitrary, $(M_n)$ are iid copies of a non--degenerate random variable $M$, $0\le M\le1$, and $q>0$ is a…
Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty…
We analyse the probability densities of daily rainfall amounts at a variety of locations on the Earth. The observed distributions of the amount of rainfall fit well to a q-exponential distribution with exponent q close to q=1.3. We discuss…
As well known, the generalized Langevin equation with a memory kernel decreasing at large times as an inverse power law of time describes the motion of an anomalously diffusing particle. Here, we focus attention on some new aspects of the…
Many recent large-scale studies of interaction networks have focused on networks of accumulated contacts. In this paper we explore social networks of ongoing relationships with an emphasis on dynamical aspects. We find a distribution of…
This paper studies the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. The randomness of market trade values and volumes during the averaging interval {\Delta} results in…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…
We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of…
In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall…
The timing patterns of human communication in social networks is not random. On the contrary, communication is dominated by emergent statistical laws such as non-trivial correlations and clustering. Recently, we found long-term correlations…
The distribution of intervals between human actions such as email posts or keyboard strokes demonstrates distinct properties at short vs long time scales. For instance, at long time scales, which are presumably controlled by complex process…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
The average time between two occurrences of the same event, referred to as its return time (or return period), is a useful statistical concept for practical applications. For instance insurances or public agency may be interested by the…
We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show…
We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbounded intensity, not of L\'evy-driven type…
Extreme value statistics, or extreme statistics for short, refers to the statistics that characterizes rare events of either unusually high or low intensity: climate disasters like floods following extremely intense rains are among the…
We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount…