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We analyze the Standard & Poor's 500 stock market index from the last 22 years. The probability density function of price returns exhibits two well-distinguished regimes with self-similar structure: the first one displays strong…
Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
It has been proved by Bovier & Hartung [Elect. J. Probab. 19 (2014)] that the maximum of a variable-speed branching Brownian motion (BBM) in the weak correlation regime converges to a randomly shifted Gumbel distribution. The random shift…
We propose a deep learning approach to probabilistic forecasting of macroeconomic and financial time series. Being able to learn complex patterns from a data rich environment, our approach is useful for a decision making that depends on…
This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation…
\cite{tsagris2025a} proposed the generalized circular projected Cauchy (GCPC) distribution, whose special case is the wrapped Cauchy distribution. In this paper we first derive the relationship with the wrapped Cauchy distribution, and then…
We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method…
For a real-valued one dimensional diffusive strict local martingale,, we provide a set of smooth functions in which the Cauchy problem has a unique classical solution under a local H\"older condition. Under the weaker Engelbert-Schmidt…
We consider a semimartingale market model when the underlying diffusion has a singular volatility matrix and compute the hedging portfolio for a given payoff function. Recently, the representation problem for such degenerate diffusions with…
We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii)…
We introduce and establish the main properties of QHawkes ("Quadratic" Hawkes) models. QHawkes models generalize the Hawkes price models introduced in E. Bacry et al. (2014), by allowing all feedback effects in the jump intensity that are…
Predicting extreme events in nonlinear dynamical systems is challenging due to a limited understanding of their statistical properties. This study numerically and theoretically investigates the statistical properties of infinite-modal maps…
A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution…
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic…
Diffusion processes with branching play an important role in statistical dynamics. They are a common approach to the computing of quantum mechanical groundstates, and serve as models for population dynamics and as physical pictures for…
This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…
Many natural and socio-economic systems are characterized by power-law distributions that make the occurrence of extreme events not negligible. Such events are sometimes referred to as Black Swans, but a quantitative definition of a Black…