Monte-Carlo simulation of a stochastic differential equation

2017 ◽  
Vol 19 (12) ◽  
pp. 125001 ◽  
Author(s):  
Arif ULLAH ◽  
Majid KHAN ◽  
M KAMRAN ◽  
R KHAN ◽  
Zhengmao SHENG
Keyword(s):  
Differential Equation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation

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.

scholarly journals Ice Gouge Depth Determination Via an Efficient Stochastic Dynamics Technique

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Nikolaos Gazis ◽  
Ioannis A. Kougioumtzoglou ◽  
Edoardo Patelli
Keyword(s):  
Differential Equation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Path Integral ◽  
Stochastic Dynamics ◽  
Simplified Model ◽  
Preliminary Design ◽  
Depth Determination ◽  
Nonlinear Stochastic Differential Equation

A simplified model of the motion of a grounding iceberg for determining the gouge depth into the seabed is proposed. Specifically, taking into account uncertainties relating to the soil strength, a nonlinear stochastic differential equation governing the evolution of the gouge length/depth in time is derived. Further, a recently developed Wiener path integral (WPI) based approach for solving approximately the nonlinear stochastic differential equation is employed; thus, circumventing computationally demanding Monte Carlo based simulations and rendering the approach potentially useful for preliminary design applications. The accuracy/reliability of the approach is demonstrated via comparisons with pertinent Monte Carlo simulation (MCS) data.

An approximation result and Monte Carlo simulation of the adapted solution of the one-dimensional backward stochastic differential equation

2018 ◽  
Vol 26 (3) ◽  
pp. 131-142
Author(s):  
A. Sghir ◽  
D. Seghir ◽  
S. Hadiri
Keyword(s):  
Differential Equation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Backward Stochastic Differential Equation ◽  
Multidimensional Case ◽  
Reference Trajectory ◽  
Approximation Result ◽  
One Dimensional ◽  
The One

Abstract In this paper, we give an approximation result for the adapted solution of the one-dimensional backward stochastic differential equation driven by a one-dimensional Brownian motion (BSDE for short). To prove our main result, we linearize the generator of the BSDE around a deterministic nominal reference trajectory by using a Taylor series expansion. We then find an approximate linear model of the BSDE. A test of our method is given with a numerical scheme driven by the Monte Carlo simulation. We believe that our result is new and valid for the multidimensional case.

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.

Quasi-Monte Carlo simulation of differential equations

2017 ◽  
Vol 23 (4) ◽  
Author(s):  
Aïcha Chouraqui ◽  
Christian Lécot ◽  
Bachir Djebbar
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Differential Equations ◽  
Numerical Solution ◽  
Quasi Monte Carlo

AbstractWe are interested in the numerical solution of the ordinary differential equation

Finite element based Monte Carlo simulation of options on Lévy driven assets

2018 ◽  
Vol 05 (01) ◽  
pp. 1850013 ◽  
Author(s):  
Patrik Karlsson
Keyword(s):  
Differential Equation ◽  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Transition Matrix ◽  
Simulation Algorithm ◽  
Option Prices ◽  
European Options ◽  
Inverse Transition

This paper extends the simulation algorithm by Andreasen and Huge (2011) to the simulation of option prices and deltas on Lévy driven assets where the simulation is performed relying on the inverse transition matrix of the discretized partial integro differential equation (PIDE). We demonstrate how one can get accurate prices and deltas of European options on VG and CGMY via Monte Carlo simulations.

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.

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