Under proper scaling and distributional assumptions, we prove the convergence in the Skorokhod space endowed with the $M_1$-topology of a sequence of stochastic integrals of a deterministic function driven by a time-changed ...

The speed of many one-line transformation methods for the production of, for example, Lévy alpha-stable random numbers, which generalize Gaussian ones, and Mittag-Leffler random numbers, which generalize exponential ones, ...

We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence ...

The relationship between quadratic variation for compound renewal processes and M-Wright functions is discussed. The convergence of quadratic variation is investigated both as a random variable (for given t) and as a ...

A simulation of high-frequency market data is performed with the Genoa Artificial Stock Market. Heterogeneous agents trade a risky asset in exchange for cash. Agents have zero intelligence and issue random limit or market ...

In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of ...

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded ...

We explore the spatial complexity of Conway's "Game of Life," a prototypical cellular automaton by means of a geometrical procedure generating a two-dimensional random walk from a bidimensional lattice with periodical ...

This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. It begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension ...

The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied ...