Related papers: Beyond complex Langevin equations I: two simple ex…
In recent years, several fractional generalizations of the usual Kramers-Fokker-Planck equation have been presented. Using an idea of Fogedby [H.C. Fogedby, Phys. Rev. E {\bf 50}, 041103 (1994), we show how these equations are related to…
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 consider the Cauchy problem for a pseudo-differential operator which has a translation-invariant and analytic symbol. For a certain set of initial conditions, a formal solution is obtained by a perturbative expansion. The series so…
Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with H\"older continuous paths on $[0,T]$ ($T > 0$). Taking that equation in rough paths sense only gives local existence…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
The analysis of many problems of interest associated with Markov chains, e.g. stationary distributions, moments of first passage time distributions and moments of occupation time random variables, involves the solution of a system of linear…
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…
A generalized Langevin equation is suggested to describe a system with memory($u(t,t') = \frac{1}{\Gamma (\nu )}(t - t')^\nu $) as well as with positive and negative damping. The equation can be transformed into the Fokker-Planck equation…
Bayesian inference plays a central role in scientific and engineering applications by enabling principled reasoning under uncertainty. However, sampling from generic probability distributions remains a computationally demanding task. This…
We prove results concerning the representation of a given distribution by means of a given random quantity. The existence of a solution to this problem is related to the notion of conglomerability, originally introduced by Dubins to study…
Many inverse problems focus on recovering a quantity of interest that is a priori known to exhibit either discontinuous or smooth behavior. Within the Bayesian approach to inverse problems, such structural information can be encoded using…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations…
Extremization of the Boltzmann-Gibbs (BG) entropy under appropriate norm and width constraints yields the Gaussian distribution. Also, the basic solutions of the standard Fokker-Planck (FP) equation (related to the Langevin equation with…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
We consider Gaussian ensembles of m N x N complex matrices. We identify an enhanced symmetry in the system and the resultant closed subsector, which is naturally associated with the radial sector of the theory. The density of radial…
We investigate a simple model using the numerical simulation in the complex Langevin equation (CLE) and the analytical approximation with the Gaussian Ansatz. We find that the Gaussian Ansatz captures the essential and even quantitative…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…