scholarly journals Invariant Measures of Ultimately Bounded Stochastic Processes

1973 ◽  
Vol 49 ◽  
pp. 149-153 ◽  
Author(s):  
Yoshio Miyahara
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Stochastic Processes ◽  
Invariant Measures ◽  
Ultimate Boundedness

The author discussed in [4] the ultimate boundedness of a system which is governed by a stochastic differential equation

scholarly journals The probabilistic approach to the analysis of the limiting behavior of an integro-diffebential equation depending on a small parameter, and its application to stochastic processes

1994 ◽  
Vol 7 (1) ◽  
pp. 25-31
Author(s):  
O. V. Borisenko ◽  
A. D. Borisenko ◽  
I. G. Malyshev
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Stochastic Differential Equation ◽  
Small Parameter ◽  
Stochastic Processes ◽  
Probabilistic Approach ◽  
Problem Solution ◽  
Poisson Measure ◽  
Limiting Behavior ◽  
The Cauchy Problem

Using connection between stochastic differential equation with Poisson measure term and its Kolmogorov's equation, we investigate the limiting behavior of the Cauchy problem solution of the integro differential equation with coefficients depending on a small parameter. We also study the dependence of the limiting equation on the order of the parameter.

scholarly journals Optimal control of ultimately bounded stochastic processes

1974 ◽  
Vol 53 ◽  
pp. 157-170
Author(s):  
Yoshio Miyahara
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Markov Process ◽  
Stochastic Differential Equation ◽  
Stochastic Processes ◽  
Wiener Process ◽  
Admissible Control ◽  
Standard Wiener Process ◽  
The Cost

We shall consider the optimal control for a system governed by a stochastic differential equationwhere u(t, x) is an admissible control and W(t) is a standard Wiener process. By an optimal control we mean a control which minimizes the cost and in addition makes the corresponding Markov process stable.

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.

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