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A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
This paper proposes a generalized binomial distribution with four parameters, which is derived from the finite capacity queueing system with state-dependent service and arrival rates. This distribution is also generated from the conditional…
This paper investigates a novel a-posteriori variance reduction approach in Monte Carlo image synthesis. Unlike most established methods based on lateral filtering in the image space, our proposition is to produce the best possible estimate…
The mutual derivation between arbitrary distribution forms of momenta and momentum components of particles produced in an isotropic emission source are systematically studied in terms of probability theory and mathematical statistics. The…
Monte Carlo methods are state-of-the-art when it comes to dosimetric computations in radiotherapy. However, the execution time of these methods suffers in high-collisional regimes. We address this problem by introducing a kinetic-diffusion…
Most meso-scale simulation methods assume Gaussian distributions of velocity-like quantities. These quantities are not true velocities, however, but rather time-averaged velocities or displacements of particles. We show that there is a…
A cascade model is described based on multiplier distributions determined from 3D direct numerical simulations (DNS) of turbulent particle laden flows, which include two-way coupling between the phases at global mass loadings equal to…
Kinetic plasma studies often require computing integrals of the velocity distribution over a complex-valued pole. The standard method is to solve the integral in the complex plane using the Plemelj theorem, resulting in the standard plasma…
In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the…
The naive importance sampling (IS) estimator generally does not work well in examples involving simultaneous inference on several targets, as the importance weights can take arbitrarily large values, making the estimator highly unstable. In…
X-ray dose constantly gains interest in the interventional suite. With dose being generally difficult to monitor reliably, fast computational methods are desirable. A major drawback of the gold standard based on Monte Carlo (MC) methods is…
In this paper we consider inhomogeneous Galton-Watson trees, and derive various moments for such processes: the number of vertices, the number of leaves, and the height of the tree. Also we make a simple condition of finiteness. We use…
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
We propose a computationally efficient random walk on a convex body which rapidly mixes and closely tracks a time-varying log-concave distribution. We develop general theoretical guarantees on the required number of steps; this number can…
We construct in the small-time setting the upper and lower estimates for the transition probability density of a L\'evy process in $\rn$. Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…
This article introduces a method for adjusting macro-particle weights within a particle distribution while preserving statistical and physical properties. The method allows the weights of the new macro-particle distribution to be determined…
We apply extensive Monte Carlo simulations to study the probability distribution $P(m)$ of the order parameter $m$ for the simple cubic Ising model with periodic boundary condition at the transition point. Sampling is performed with the…
This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP…