scholarly journals Calculation of Probability of the Exit of a Stochastic Process from a Band by Monte-Carlo Method: A Wiener-Hopf Factorization

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 581
Author(s):  
Beliavsky ◽  
Danilova ◽  
Ougolnitsky
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Stochastic Differential Equation ◽  
Random Partition ◽  
Numerical Examples ◽  
Girsanov Transform ◽  
The Monte Carlo Method

This paper considers a method of the calculation of probability of the exit from a band of the solution of a stochastic differential equation. The method is based on the approximation of the solution of the considered equation by a process which is received as a concatenation of Gauss processes, random partition of the interval, Girsanov transform and Wiener-Hopf factorization, and the Monte-Carlo method. The errors of approximation are estimated. The proposed method is illustrated by numerical examples.

scholarly journals Monte-Carlo Galerkin Approximation of Fractional Stochastic Integro-Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Abdallah Ali Badr ◽  
Hanan Salem El-Hoety
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Galerkin Method ◽  
Existence And Uniqueness ◽  
Galerkin Approximation ◽  
Integro Differential Equation ◽  
Uniqueness Of The Solution ◽  
Time Continuum

A stochastic differential equation, SDE, describes the dynamics of a stochastic process defined on a space-time continuum. This paper reformulates the fractional stochastic integro-differential equation as a SDE. Existence and uniqueness of the solution to this equation is discussed. A numerical method for solving SDEs based on the Monte-Carlo Galerkin method is presented.

A Stochastic Approach for Radiative Exchange in Enclosures With Directional-Bidirectional Properties

1986 ◽  
Vol 108 (2) ◽  
pp. 264-270 ◽  
Author(s):  
M. H. N. Naraghi ◽  
B. T. F. Chung
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat ◽  
Transition Probabilities ◽  
Stochastic Approach ◽  
Numerical Examples ◽  
The Monte Carlo Method ◽  
Transfer Problems ◽  
Radiative Exchange

The concept of multiple Markov chains is applied to the study of radiative heat transfer problems. A stochastic method for calculating radiative interchange in enclosures consisting of a number of isothermal surfaces with directional-bidirectional properties is developed. In this work, the Monte Carlo method is employed for calculating the multiple transition probabilities. Numerical examples have been presented to demonstrate the usefulness of the present approach.

scholarly journals Minimax Decision for the Reliability of Aircraft Fleet With and Without Information Exchange

2016 ◽  
Vol 3 (1) ◽  
pp. 24-30
Author(s):  
Sergejs Tretjakovs ◽  
Jurijs Paramonovs
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Failure Probability ◽  
Information Exchange ◽  
Human Factor ◽  
Fatigue Cracks ◽  
Scientific Article ◽  
Numerical Examples ◽  
The Monte Carlo Method ◽  
New Type

Abstract The scientific article addresses the dependence of aircraft fleet safety on the human factor. The article demonstrates the significance of information exchange concerning the open fatigue cracks, which is necessary to bring a new type of aircraft into operation. The article provides numerical examples obtained by means of the Monte Carlo method and considers the dependences of failure probability on various factors.

Simulating oxygen transport in the microcirculation by Monte Carlo methods

SIMULATION ◽  
1970 ◽  
Vol 15 (5) ◽  
pp. 206-212 ◽  
Author(s):  
Michael R. Halberg ◽  
Duane F. Bruley ◽  
Melvin H. Knisely
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Oxygen Transport ◽  
Nonlinear Partial Differential Equation ◽  
Dissociation Curve ◽  
Partial Differential ◽  
Oxygen Dissociation ◽  
The Monte Carlo Method

Oxygen transport in the human cerebral cortex has been simulated previously by considering a single straight capillary and a concentric tissue cylinder as a representa tive sample (the Krogh tissue cylinder). The same geo metric model has been assumed for this study because of its probable accuracy and to allow comparison with previous calculations. Because of the nonlinear equilibrium relationship be tween dissolved and hemoglobin-bound oxygen (the oxy gen dissociation curve), a differential mass balance yields a nonlinear partial differential equation describing oxy gen transport in the capillary. In the tissue a constant consumption rate is assumed and a linear partial differ ential equation results. The tissue equation and the capillary equation are solved simultaneously, to account for capillary-tissue interaction, thus giving axial and radial oxygen partial pressure profiles for the total system. The Monte Carlo method has been employed to solve the resulting set of equations on a digital computer. This technique involves a numerical scheme wherein a process is simulated directly by a random walk phenomenon (Markov process). A particular advantage of this method is that solutions may be obtained for one point in space independently of all others. Therefore, an analysis of the transient response of the "lethal corner" is possible with out solving for the entire mesh. Computation time with the Monte Carlo method was considerably less than that with standard deterministic numerical calculation tech niques. Two models were considered. In the first model the oxygen dissociation curve was linearized, thus giving a linear partial differential equation describing oxygen transport in the capillary. The second model considered the nonlinear nature of the oxygen dissociation curve, and a nonlinear partial differential equation was ob tained. However, because of difficulties with the Monte Carlo method, it was necessary to solve the equations in a quasi-nonlinear manner. For both the linear and the quasi-nonlinear models, solutions were obtained for the steady state with normal conditions and for dynamic cases. Perturbations of ar terial-oxygen partial pressure and blood flow rate were forced, and the behavior of the system was determined. The pure diffusional model checked with previous de terministic calculations demonstrating very rapid re sponse with time constants in the order of 2 seconds. However, the shapes of the intracapillary and tissue oxy gen tension profiles differed somewhat and no allow ances were made for autoregulatory phenomena such as varying flow rates.

scholarly journals Generalized mathematical model of cancer heterogeneity

2020 ◽  
Author(s):  
Motohiko Naito
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Model ◽  
Stochastic Process ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Cancer Growth ◽  
Cancer Heterogeneity ◽  
Growth Properties

AbstractThe number of reports on mathematical modeling related to oncology is increasing with advances in oncology. Even though the field of oncology has developed significantly over the years, oncology-related experiments remain limited in their ability to examine cancer. To overcome this limitation, in this study, a stochastic process was incorporated into conventional cancer growth properties to obtain a generalized mathematical model of cancer growth. Further, an expression for the violation of symmetry by cancer clones that leads to cancer heterogeneity was derived by solving a stochastic differential equation. Monte Carlo simulations of the solution to the derived equation validate the theories formulated in this study. These findings are expected to provide a deeper understanding of the mechanisms of cancer growth, with Monte Carlo simulation having the potential of being a useful tool for oncologists.

UGR CALCULATION BASED ON THE LUMINANCE SPATIAL-ANGULAR DISTRIBUTION

2020 ◽  
Vol 2020 (4) ◽  
pp. 25-32
Author(s):  
Viktor Zheltov ◽  
Viktor Chembaev
Keyword(s):  
Monte Carlo ◽  
Angular Distribution ◽  
Monte Carlo Method ◽  
Visual Task ◽  
New Method ◽  
Lighting System ◽  
Preliminary Assessment ◽  
System A ◽  
The Monte Carlo Method

The article has considered the calculation of the unified glare rating (UGR) based on the luminance spatial-angular distribution (LSAD). The method of local estimations of the Monte Carlo method is proposed as a method for modeling LSAD. On the basis of LSAD, it becomes possible to evaluate the quality of lighting by many criteria, including the generally accepted UGR. UGR allows preliminary assessment of the level of comfort for performing a visual task in a lighting system. A new method of "pixel-by-pixel" calculation of UGR based on LSAD is proposed.

PSHA software review based on the Monte Carlo method

2020 ◽  
pp. 14-24
Author(s):  
V.A. Mironov ◽  
S.A. Peretokin ◽  
K.V. Simonov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Seismic Hazard ◽  
Hazard Analysis ◽  
Software Review ◽  
Seismic Hazard Analysis ◽  
Probabilistic Seismic Hazard ◽  
Test Calculation ◽  
Seismic Surveys ◽  
The Monte Carlo Method

The article is a continuation of the software research to perform probabilistic seismic hazard analysis (PSHA) as one of the main stages in engineering seismic surveys. The article provides an overview of modern software for PSHA based on the Monte Carlo method, describes in detail the work of foreign programs OpenQuake Engine and EqHaz. A test calculation of seismic hazard was carried out to compare the functionality of domestic and foreign software.

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