Comparison of Markov Chain and Stochastic Differential Equation Population Models Under Higher-Order Moment Closure Approximations

2010 ◽  
Vol 28 (6) ◽  
pp. 907-927 ◽  
Author(s):  
Amy J. Ekanayake ◽  
Linda J. S. Allen
Keyword(s):  
Differential Equation ◽  
Markov Chain ◽  
Stochastic Differential Equation ◽  
Higher Order ◽  
Population Models ◽  
Moment Closure ◽  
Order Moment ◽  
Closure Approximations ◽  
Moment Closure Approximations

scholarly journals Moment-closure approximations for discrete adaptive networks

2014 ◽  
Vol 267 ◽  
pp. 68-80 ◽  
Author(s):  
G. Demirel ◽  
F. Vazquez ◽  
G.A. Böhme ◽  
T. Gross
Keyword(s):  
Moment Closure ◽  
Adaptive Networks ◽  
Closure Approximations ◽  
Moment Closure Approximations

scholarly journals Diagnostics for assessing the linear noise and moment closure approximations

2016 ◽  
Vol 15 (5) ◽  
Author(s):  
Colin S. Gillespie ◽  
Andrew Golightly
Keyword(s):  
Region Of Interest ◽  
Moment Closure ◽  
Diagnostic Tools ◽  
Approximate Algorithms ◽  
Parameter Region ◽  
Normality Assumption ◽  
Closure Approximations ◽  
Simulation Based ◽  
Space Filling Design ◽  
Moment Closure Approximations

AbstractSolving the chemical master equation exactly is typically not possible, so instead we must rely on simulation based methods. Unfortunately, drawing exact realisations, results in simulating every reaction that occurs. This will preclude the use of exact simulators for models of any realistic size and so approximate algorithms become important. In this paper we describe a general framework for assessing the accuracy of the linear noise and two moment approximations. By constructing an efficient space filling design over the parameter region of interest, we present a number of useful diagnostic tools that aids modellers in assessing whether the approximation is suitable. In particular, we leverage the normality assumption of the linear noise and moment closure approximations.

A Class of Jump-Diffusion Stochastic Differential System Under Markovian Switching and Analytical Properties of Solutions

2020 ◽  
Vol 8 (1) ◽  
pp. 17-32
Author(s):  
Xiangdong Liu ◽  
Zeyu Mi ◽  
Huida Chen
Keyword(s):  
Differential Equation ◽  
Markov Chain ◽  
Stochastic Differential Equation ◽  
Differential System ◽  
Numerical Solutions ◽  
Jump Diffusion ◽  
Markovian Switching ◽  
Analytical Properties ◽  
Global Nature ◽  
First Moment

AbstractOur article discusses a class of Jump-diffusion stochastic differential system under Markovian switching (JD-SDS-MS). This model is generated by introducing Poisson process and Markovian switching based on a normal stochastic differential equation. Our work dedicates to analytical properties of solutions to this model. First, we give some properties of the solution, including existence, uniqueness, non-negative and global nature. Next, boundedness of first moment of the solution to this model is considered. Third, properties about coefficients of JD-SDS-MS is proved by using a right continuous markov chain. Last, we study the convergence of Euler-Maruyama numerical solutions and apply it to pricing bonds.

scholarly journals From Markovian to pairwise epidemic models and the performance of moment closure approximations

2011 ◽  
Vol 64 (6) ◽  
pp. 1021-1042 ◽  
Author(s):  
Michael Taylor ◽  
Péter L. Simon ◽  
Darren M. Green ◽  
Thomas House ◽  
Istvan Z. Kiss
Keyword(s):  
Epidemic Models ◽  
Moment Closure ◽  
Closure Approximations ◽  
Moment Closure Approximations

scholarly journals Toward a Wong–Zakai Approximation for Big Order Generators

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1893
Author(s):  
Rémi Léandre
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Stochastic Differential Equation ◽  
Finite Energy ◽  
Higher Order ◽  
Semi Group

We give a new approximation with respect of the traditional parametrix method of the solution of a parabolic equation whose generator is of big order and under the Hoermander form. This generalizes to a higher order generator the traditional approximation of Stratonovitch diffusion which put in relation random ordinary differential equation (the leading process is random and of finite energy. When a trajectory of it is chosen, the solution of the equation is defined) and stochastic differential equation (the leading process is random and only continuous and we cannot choose a path in the solution which is only almost surely defined). We consider simple operators where the computations can be fully performed. This approximation fits with the semi-group only and not for the full path measure in the case of a stochastic differential equation.

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