Related papers: Simulation using random numbers
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
This is a guide to the mathematical theory of Brownian motion and related stochastic processes, with indications of how this theory is related to other branches of mathematics, most notably the classical theory of partial differential…
Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…
In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…
A brief introduction to the technique of Monte Carlo simulations in statistical physics is presented. The topics covered include statistical ensembles random and pseudo random numbers, random sampling techniques, importance sampling, Markov…
A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…
In this paper, we suggest a novel sampling method for Monte Carlo molecular simulations. In order to perform efficient sampling of molecular systems, it is advantageous to avoid extremely high energy configurations while also retaining the…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
We introduce a technique to merge two biased Brownian motions into a single regular process. The outcome follows a stochastic differential equation with a constant diffusion coefficient and a non-linear drift. The emerging stochastic…
An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…
The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…
Motivated by contemporary and rich applications of anomalous diffusion processes we propose a new statistical test for fractional Brownian motion, which is one of the most popular models for anomalous diffusion systems. The test is based on…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential…
This paper is a tutorial and literature review on sampling algorithms. We have two main types of sampling in statistics. The first type is survey sampling which draws samples from a set or population. The second type is sampling from…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
We present an intuitive, conceptual, but semi-rigorous introduction to the celebrated Markov Chain Monte Carlo method using a simple model of population dynamics as our motivation and focusing on a few elementary distributions.…