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We empirically analyze the reversion of financial market trends with time horizons ranging from minutes to decades. The analysis covers equities, interest rates, currencies and commodities and combines 14 years of futures tick data, 30…

We report the experimental observation of $1/f^{\alpha}$ noise in quasi-bidimensionnal turbulence of an electromagnetically forced flow. The large scale velocity $U_L$ exhibits this power-law spectrum with $\alpha \simeq 0.7$ over a range…

Periodic patterns are fundamental cues in multimedia signals and systems, including repetitive motion in video (e.g., gait cycles), rhythmic and pitch-related structure in audio, and recurring textures in image sequences. When such…

It is well known that a random multiplicative process with weak additive noise generates a power-law probability distribution. It has recently been recognized that this process exhibits another type of power law: the moment of the…

We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self…

The law of one price (LOP) broadly asserts that identical financial flows should command the same price. We show that, when properly formulated, LOP is the minimal condition for a well-defined mean-variance portfolio selection framework…

While preserving the privacy of federated learning (FL), differential privacy (DP) inevitably degrades the utility (i.e., accuracy) of FL due to model perturbations caused by DP noise added to model updates. Existing studies have considered…

Stylized facts of empirical assets log-returns $Z$ include the existence of (semi) heavy tailed distributions $f_Z(z)$ and a non-linear spectrum of Hurst exponents $\tau(\beta)$. Empirical data considered are daily prices of 10 large…

We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by [Lux and Sornette, 1999] that the distribution of returns is a power law with exponent less than 1, in contradiction with…

Financial markets exhibit complex dynamics where localized events trigger ripple effects across entities. Previous event studies, constrained by static single-company analyses and simplistic assumptions, fail to capture these ripple…

Maximum likelihood estimation applied to high-frequency data allows us to quantify intermittency in the fluctu- ations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency…

We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that…

The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What it is well…

We revisit the time evolution of a flat and non-flat direction system during inflation. In order to take into account quantum noises in the analysis, we base on stochastic formalism and solve coupled Langevin equations numerically. We focus…

Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…

Nonlinear stochastic differential equations generating signals with 1/f spectrum have been used so far to describe socio-economical systems. In this paper we consider the motion of a Brownian particle in an inhomogeneous environment such…

Instantaneous noise-based logic can avoid time-averaging, which implies significant potential for low-power parallel operations in beyond-Moore-law-chips. However, the universe (uniform superposition) will be zero with high probability…

The Period-Luminosity (PL) relation is usually derived using time-averaged magnitudes, which require multiple-epoch observations to determine periods and adequately sample the light curves. Although single-epoch observations are more…

The low-frequency noise (LF-noise) of deep submicron MOSFETs is experimentally studied with special emphasis on yield relevant parameter scattering. A novel modeling approach is developed which includes detailed consideration of statistical…