scholarly journals On the approximation of stochastic differential equation and on stroock-varadhan's support theorem

1990 ◽  
Vol 19 (1) ◽  
pp. 65-70 ◽  
Author(s):  
I. Gyöngy ◽  
T. Pröhle
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Support Theorem

scholarly journals Stroock-Varadhan support theorem for random evolution equation in Besov-Orlicz spaces

2020 ◽  
pp. 187-203
Author(s):  
Jocelyn Hajaniaina Andriatahina ◽  
Dina Miora Rakotonirina ◽  
Toussaint Joseph Rabeherimanana
Keyword(s):  
Differential Equation ◽  
Evolution Equation ◽  
Stochastic Differential Equation ◽  
Stochastic Processes ◽  
Orlicz Space ◽  
Modulus Of Continuity ◽  
Orlicz Spaces ◽  
Random Evolution ◽  
Support Theorem ◽  
The Family

We consider the family of stochastic processes $X=\{X_t, t\in [0;1]\}\,,$ where $X$ is the solution of the It\^{o} stochastic differential equation \[dX_t = \sigma(X_t, Z_t)dW_t + b(X_t,Y_t) dt \hspace*{2cm}\] whose coefficients Lipschitzian depend on $Z=\{Z_t, t\in [0;1]\} $ and $Y=\{Y_t, t\in [0;1]\}$. We prove that the trajectories of $X$ a.s. belong to the Besov-Orlicz space defined by the f nction $M(x)=e^{x^2}-1$ and the modulus of continuity $\omega(t)=\sqrt{t\log(1/t)}$. The aim of this work is to characterize the support of the law $X$ in this space.

On Approximate Large Deviations for 1D Diffusion

2003 ◽  
Vol 10 (2) ◽  
pp. 381-399
Author(s):  
A. Yu. Veretennikov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Approximation Scheme ◽  
Sufficient Conditions ◽  
Rate Function ◽  
Euler Approximation ◽  
One Dimensional

Abstract We establish sufficient conditions under which the rate function for the Euler approximation scheme for a solution of a one-dimensional stochastic differential equation on the torus is close to that for an exact solution of this equation.

Large deviations and Berry–Esseen inequalities for estimators in nonhomogeneous diffusion driven by fractional Brownian motion

2020 ◽  
Vol 28 (3) ◽  
pp. 183-196
Author(s):  
Kouacou Tanoh ◽  
Modeste N’zi ◽  
Armel Fabrice Yodé
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Maximum Likelihood ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Maximum Likelihood Estimator ◽  
Bayes Estimator ◽  
Likelihood Estimator

AbstractWe are interested in bounds on the large deviations probability and Berry–Esseen type inequalities for maximum likelihood estimator and Bayes estimator of the parameter appearing linearly in the drift of nonhomogeneous stochastic differential equation driven by fractional Brownian motion.

scholarly journals A spatially varying stochastic differential equation model for animal movement

2018 ◽  
Vol 12 (2) ◽  
pp. 1312-1331 ◽  
Author(s):  
James C. Russell ◽  
Ephraim M. Hanks ◽  
Murali Haran ◽  
David Hughes
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Animal Movement ◽  
Equation Model ◽  
Differential Equation Model ◽  
Spatially Varying
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