Now showing items 1-17 of 17

• #### A class of CTRWs: Compound fractional poisson processes ﻿

(2011-12-31)
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 ...
• #### A functional limit theorem for stochastic integrals driven by a time-changed symmetric sigma-stable Levy process ﻿

(2014-12-31)
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 ...
• #### A stylized model for the continuous double auction ﻿

(2012-12-31)
A stylized phenomenological model for the continuous double auction is introduced. This model is equivalent to two uncoupled M/M/1 queues. The conditions for statistical equilibrium (ergodicity) are derived. The results ...
• #### Emerging properties of financial time series in the "game of Life" ﻿

(2011-12-31)
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 ...
• #### Ergodic transition in a simple model of the continuous double auction ﻿

(2014-12-31)
We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues. The continuous double auction defines a continuous-time random walk for trade ...
• #### Fine structure of spectral properties for random correlation matrices: An application to financial markets ﻿

(2011-12-31)
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 ...
• #### Full characterization of the fractional Poisson process ﻿

(2011-12-31)
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 ...
• #### Large-scale simulations of synthetic markets ﻿

(2015-10-08)
High-frequency trading has been experiencing an increase of interest both for practical purposes within nancial institutions and within academic research; recently, the UK Government O ce for Science reviewed the state ...
• #### Low-traffic limit and first-passage times for a simple model of the continuous double auction ﻿

(2017-05)
We consider a simplified model of the continuous double auction where prices are integers varying from 1 to $N$ with limit orders and market orders, but quantity per order limited to a single share. For this model, the ...
• #### Modeling non-stationarities in high-frequency financial time series ﻿

(2019-01)
We study tick-by-tick financial returns for the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We confirm previously detected non-stationarities. Scaling properties reported before for other high-frequency ...
• #### On the convergence of quadratic variation for compound fractional poisson processes ﻿

(2012-12-31)
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 ...
• #### On the non-stationarity of financial time series: Impact on optimal portfolio selection ﻿

(2012-12-31)
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 ...
• #### Random numbers from the tails of probability distributions using the transformation method ﻿

(2013-12-31)
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, ...
• #### Semi-markov graph dynamics ﻿

(2011-12-31)
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 ...
• #### Statistical analysis and agent-based microstructure modeling of high-frequency financial trading ﻿

(2012-12-31)
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 ...
• #### Velocity and energy distributions in microcanonical ensembles of hard spheres ﻿

(2015-12-31)
In a microcanonical ensemble (constant NVE, hard reflecting walls) and in a molecular dynamics ensemble (constant NVEPG, periodic boundary conditions) with a number N of smooth elastic hard spheres in a d-dimensional volume ...
• #### Wealth distribution and the Lorenz curve: a finitary approach ﻿

(2015-12-31)
We use three stochastic games for the wealth of economic agents which may be at work in a real economy and we derive their statistical equilibrium distributions. Based on a heuristic argument, we assume that the expected ...