Volume 31, Issue 2

This article investigates the localized air quality of the workplace and its impacts on the stochastic behaviour of aerosol deposition. Related to the same, the dewpoint (DPT), wet bulb (WBT) and dry bulb (DBT) temperatures, vapour pressure, and relative and specific humidities of the air are being tested. The given problem investigates the regional and total deposition of aerosol particles in the extrathoracic (Ex), bronchioles (Br) and alveolar sacs (A) of the subjects working in the bioenergy plant. The oral and nasal (n) pathways were considered for the air to enter the extrathoracic region of the human body. The algorithm based on the Monte-Carlo technique is written on Rust version 1.79.0 to calculate the deposition fraction of aerosol particles in the human lungs. The particle is assumed to have a spherical geometry. Only the diffusion of water vapour onto the surface of aerosol is the limiting factor for the growth of aerosol particles and the surface reaction is omitted. The deposition fraction of smaller-sized particles was seen to be increased with nucleation in the Ex region. Similarly, the change in the dew point of air also favoured the likelihood of deposition of the aerosol particle in the Ex region. As compared to the nasal pathway, the accretion of aerosol particles in the Ex region through the oral pathway declined by 35.12  to 38.33  owing to the growth of the aerosol particles with time.

In this article, Bayesian estimators of the traffic intensity (ρ) in single server Markovian ( M / M / 1 {M/M/1} ) queueing system are derived under the squared error loss function (SELF) and precautionary loss function (PLF). These Bayes estimators are derived using three different priors viz. beta, independent gamma and Jeffrey distribution. The effectiveness of the proposed Bayes estimators are compared in terms of their posterior risks. A suitable prior is chosen for Bayesian analysis using the model comparison criterion based on the Bayes factor.

Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the quality of such estimators is to consider the variance over the total number of observations. In this paper we present a procedure to compute the variance of the estimator proposed in [W. Kong and G. Valiant, Spectrum estimation from samples, Ann. Statist. 45 2017, 5, 2218–2247] for the case of Gaussian random vectors and provide a sharper bound than previously available.

A hybrid continuous Random Walk on Boundary algorithm and iterative refinement method is constructed. In this method, the density of the double layer boundary integral equation for the Laplace equation is resolved by an isotropic Random Walk on Boundary algorithm and calculated for a set of grid points chosen on the boundary. Then, a residual of the boundary integral equation is calculated deterministically, and the same boundary integral equation is solved where the right-hand side is changed with the residual function. This process is repeated several times until the desired accuracy is achieved. This method is compared against the standard Random Walk on Boundary algorithm in terms of their labor intensity. Simulation experiments have shown that the new method is about 200 times more efficient, and this advantage increases with the increase of the desired accuracy. It is noteworthy that the new hybrid algorithm, unlike the standard Random Walk on Boundary algorithm, solves the Laplace equation efficiently also in non-convex domains.

This article continues the research on combined stochastic-deterministic iterative algorithms for solving large system of linear algebraic equations we developed in our previous study [K. K. Sabelfeld and G. Agarkov, Randomized vector algorithm with iterative refinement for solving boundary integral equations, Monte Carlo Methods Appl. 30 2024, 4, 375–388]. In this paper we focus on two issues: Variance reduction and extension of randomized algorithms by combining them with Krylov type iterative methods like the method of conjugate gradients, the conjugate residual method, and Craig’s method. The developed randomized algorithms are applied to boundary integral equations for 2D and 3D Laplace equations.

The ability of θ-Milstein methods with θ ≥ 1 {\theta\geq 1} to capture the non-negativity and the mean-reversion property of the exact solution of the CIR model is shown. In addition, the order of convergence and the preservation of the long-term variance is studied. These theoretical results are illustrated with numerical examples.