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Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
The Complex Langevin (CL) method to simulate `complex probabilities', ideally produces expectation values for the observables that converge to a limit equal to the expectation values obtained with the original complex `probability' measure.…
We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…
In recent years it has been increasing evidence that lognormal distributions are widespread in physical and biological sciences, as well as in various phenomena of economics and social sciences. In social sciences, the appearance of…
Simulations of QCD with a finite chemical potential typically lead to a severe sign problem, prohibiting any standard Monte Carlo approach. Complex Langevin simulations provide an alternative to sample path integrals with oscillating weight…
For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the…
We study the evolution of probability distribution functions of returns, from the tick data of the Korean treasury bond (KTB) futures and the S$&$P 500 stock index, which can be described by means of the Fokker-Planck equation. We show that…
Langevin diffusion is a commonly used tool for sampling from a given distribution. In this work, we establish that when the target density $p^*$ is such that $\log p^*$ is $L$ smooth and $m$ strongly convex, discrete Langevin diffusion…
We extend the L\'evy Langevin Monte Carlo method studied by Oechsler in 2024 to the setting of a target distribution with heavy tails: Choosing a target distribution from the class of subexponential distributions we prove convergence of a…
Recently it has been questioned, notably in the context of the scalar singlet dark matter model with $m_\varphi^{ }\simeq 60$ GeV, how efficiently kinetic equilibrium is maintained if freeze-out dynamics is pushed down to low temperatures…
Stochastic quantization offers the opportunity to simulate field theories with a complex action. In some theories unstable trajectories are prevalent when a constant stepsize is employed. We construct algorithms for generating an adaptive…
Presenting a general phase approach to stochastic processes we analyze in particular the Fokker-Planck equation for the noisy Burgers equation and discuss the time dependent and stationary probability distributions. In one dimension we…
The three-dimensional SU(3) spin model is an effective Polyakov loop model for QCD at nonzero temperature and density. It suffers from a sign problem at nonzero chemical potential. We revisit this model using complex Langevin dynamics and…
A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several…
High-energy, multi-component plasmas in which pair creation and annihilation, lepton-lepton scattering, lepton-proton scattering, and Comptonization all contribute to establishing the particle and photon distributions, are present in a…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
Numerical simulations of fast remagnetization processes using the stochastic dynamics are widely used to study various magnetic systems. In this paper we first address several crucial methodological problems of such simulations: (i) the…
In this paper we introduce a generalization of classical risk measures in which the risk is represented by a step function taking two values, corresponding to two endogenously determined market regimes. This extends the traditional…
The blossoming of interest in colloids and nano-particles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to…
The sign problem appears in lattice QCD as soon as a non-zero chemical potential is introduced. This prevents direct simulations to determine the phase structure of the strongly interacting matter. Complex Langevin methods have been…