Related papers: A process-reconstruction analysis of market fluctu…
In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…
The frequency constitutes a key state variable of electrical power grids. However, as the frequency is subject to several sources of fluctuations, ranging from renewable volatility to demand fluctuations and dispatch, it is strongly…
We introduce estimators for the entropy production of a Gibbsian process based on the observation of a single or two typical trajectories. These estimators are built with adequate hitting and return times. We then study their convergence…
In [2] the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness…
We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution…
The possibility of statistical evaluation of the market completeness and incompleteness is investigated for continuous time diffusion stock market models. It is known that the market completeness is not a robust property: small random…
Motivated by stochastic models of climate phenomena, the steady-state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady-states provide a constraint on the character of…
For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal…
Various notions of fluctuations exist depending on the way one chooses to measure them. We discuss two extreme cases (continuous measurement versus long inter-measurement times) and we see their relation with entropy production and with…
As a model of market price, we introduce a new type of random walk in a moving potential which is approximated by a quadratic function with its center given by the moving average of its own trace. The properties of resulting random walks…
In a recent article [Nature 421, 130 (2003)], Plerou, Gopikrishnan and Stanley report some evidence for an intriguing two-phase behavior of financial markets when studying the distribution of volume imbalance conditional to the local…
We address microscopic, agent based, and macroscopic, stochastic, modeling of the financial markets combining it with the exogenous noise. The interplay between the endogenous dynamics of agents and the exogenous noise is the primary…
We derive a system of stochastic differential equations simulating the dynamics of the three agent groups with herding interaction. Proposed approach can be valuable in the modeling of the complex socio-economic systems with similar…
We analyze fluctuations of random walks with generally distributed increments. Integral representations for key performance measures are obtained by extending an inversion theorem of Hewitt [11] for Laplace-Stieltjes transforms. Another…
Probability distributions can be read as simple expressions of information. Each continuous probability distribution describes how information changes with magnitude. Once one learns to read a probability distribution as a measurement scale…
This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz's definition of value weighted return of a portfolio as the…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit…
Living systems often function with regulatory interactions, but the question of how activity, stochasticity and regulations work together for achieving different goals still remains puzzling. We propose a stochastic model of an active…
This paper is concerned with combined inference for point processes on the real line observed in a broken interval. For such processes, the classic history-based approach cannot be used. Instead, we adapt tools from sequential spatial point…