Related papers: A Langevin approach to multi-scale modeling
We propose to model the image differentials of astrophysical source maps by Student's t-distribution and to use them in the Bayesian source separation method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC) sampling…
In this work, we propose some numerical schemes for linear kinetic equations in the diffusion and anomalous diffusion limit. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate…
Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these…
Modelling non-homogeneous and multi-component data is a problem that challenges scientific researchers in several fields. In general, it is not possible to find a simple and closed form probabilistic model to describe such data. That is why…
We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and…
Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin…
For a system at given temperature, with energy known as a function of a set of variables, we obtain the thermal fluctuation of the evolution of the variables by replacing the phase-space with a lattice and invoking the principle of detailed…
It is not uncommon that real-world data are distributed with a long tail. For such data, the learning of deep neural networks becomes challenging because it is hard to classify tail classes correctly. In the literature, several existing…
Sampling the parameter space of artificial neural networks according to a Boltzmann distribution provides insight into the geometry of low-loss solutions and offers an alternative to conventional loss minimization for training. However,…
We consider a fixed-point equation for a non-negative integer-valued random variable, that appears in branching processes with state-independent immigration. A similar equation appears in the analysis of a single-server queue with a…
In this thesis, the tail properties of multivariate Archimedean copulas are investigated using known representation theorems involving L1-norm symmetric distributions and the Williamson d-transform. Several new results on the asymptotic…
The problem of sums of independent, identically distributed random variables with stretched-exponential tails exhibits a dynamical phase transition and has recently reemerged in the context of active transport and condensation phenomena. We…
Langevin (stochastic differential) equations are routinely used to describe particle-laden flows. They predict Gaussian probability density functions (PDFs) of a particle's trajectory and velocity, even though experimentally observed…
It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…
The upper tail of a claim size distribution of a property line of business is frequently modelled by Pareto distribution. However, the upper tail does not need to be Pareto distributed, extraordinary shapes are possible. Here, the…
Let Y be an Ornstein-Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X: dY_t=a(X_t)Y_t dt+\sigma(X_t) dW_t, Y_0=y_0. Ergodicity conditions for Y have been obtained. Here we investigate the tail propriety of the…
We study the Langevin dynamics of diffusive particles with regular pairwise interactions under mean-field scaling. By approximating empirical distributions with conditional distributions, we establish coercive and contractive properties for…
We propose a transformation capable of altering the tail properties of a distribution, motivated by extreme value theory, which can be used as a layer in a normalizing flow to approximate multivariate heavy tailed distributions. We apply…
In traditional extreme value analysis, the bulk of the data is ignored, and only the tails of the distribution are used for inference. Extreme observations are specified as values that exceed a threshold or as maximum values over distinct…
For multitype branching processes with immigration evolving in a random environment and producing a final product we find the tail distribution of the size of the final product accumulated in the system for a life period. Using this result…