Tamed Euler–Maruyama approximation for stochastic differential equations with locally Hölder continuous diffusion coefficients

2019 ◽  
Vol 145 ◽  
pp. 133-140
Author(s):  
Hoang Long Ngo ◽  
Duc Trong Luong
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Diffusion Coefficients ◽  
Hölder Continuous

scholarly journals Estimation of parameters in stochastic differential equations with two random effects

2016 ◽  
Vol 5 (2) ◽  
pp. 97
Author(s):  
Mohammed Alsukaini ◽  
Walaa Alkreemawi ◽  
Xiang-Jun Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Random Effects ◽  
Posterior Distribution ◽  
Diffusion Coefficients ◽  
Likelihood Function ◽  
Random Effect ◽  
Estimation Of Parameters ◽  
Unknown Parameters ◽  
Consistency And Asymptotic Normality

<p>In this paper we investigate consistency and asymptotic normality of the posterior distribution of the parameters in the stochastic differential equations (SDE’s) with diffusion coefficients depending nonlinearly on a random variables  and  (the random effects).The distributions of the random effects  and  depends on unknown parameters which are to be estimated from the continuous observations of the independent processes . We propose the Gaussian distribution for the random effect  and the exponential distribution for the random effect    , we obtained an explicit formula for the likelihood function and find the estimators of the unknown parameters in the random effects.</p>

Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the maximum process

2020 ◽  
Vol 26 (1) ◽  
pp. 33-47
Author(s):  
Kamal Hiderah
Keyword(s):  
Differential Equations ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Diffusion Coefficients ◽  
One Dimensional ◽  
Maximum Process ◽  
And Diffusion

AbstractThe aim of this paper is to show the approximation of Euler–Maruyama {X_{t}^{n}} for one-dimensional stochastic differential equations involving the maximum process. In addition to that it proves the strong convergence of the Euler–Maruyama whose both drift and diffusion coefficients are Lipschitz. After that, it generalizes to the non-Lipschitz case.

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