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Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some…
Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to…
In this study, we present a comprehensive analysis of the motion of a tagged monomer within a Gaussian semiflexible polymer model. We carefully derived the generalized Langevin Equation (GLE) that governs the motion of a tagged central…
Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these…
We derive an exact expression for the partition function of the su(m) Haldane-Shastry spin chain, which we use to study the density of levels and the distribution of the spacing between consecutive levels. Our computations show that when…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main…
A subdiffusion problem in which the diffusion term is related to a stable stochastic process is introduced. Linear models of these systems have been studied in a general way, but non-linear models require a more specific analysis. The model…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…
Dimerization and subsequent aggregation of polymers and biopolymers often occur under nonequilibrium conditions. When the initial state of the polymer is not collapsed or the final folded native state, the dynamics of dimerization can…
We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…
In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the…
Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…
We develop a finite-horizon model in which liquid-asset returns exhibit Levy-stable scaling on a data-driven window [tau_UV, tau_IR] and aggregate into a finite-variance regime outside. The window and the tail index alpha are identified…
After having closely re-examined the notion of a L\'evy's stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with…
Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly…
This paper is concerned with the convergence and long-term stability analysis of the feedback particle filter (FPF) algorithm. The FPF is an interacting system of $N$ particles where the interaction is designed such that the empirical…
We investigate the folding and forced-unbinding transitions of adsorbed semiflexible polymer chains using theory and simulations. These processes describe biologically relevant phenomena that include adhesive interactions between proteins…
We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the disorder) are modeled in terms of random rotations. We focus on the quenched…
In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of…