Ito Stochastic Equations Research Articles

Algebraic criteria and sufficient conditions for asymptotic stability and boundedness with probability 1 for the solutions of a system of linear stochastic difference equations

In this article, using the method of stochastic Lyapunov functions (SLF), we obtain new algebraic criteria and sufficient conditions for the asymptotic stability with probability 1 for the solutions of a system of linear stationary difference equations with random (of the type of a vector "white" sequence of random variables) coefficients, which are discrete analogs of the conditions established earlier by several authors for stochastic Ito equations with continuous time. We assume that in the absence of parametric random perturbations, an unperturbed determined system of difference equations is asymptotically Lyapunov stable (the matrix A of the system is convergent). The conditions are formulated either in terms of the negative definiteness of certain matrix relations, involving the matrix A and the matrices of the parametric perturbations Bi, i = i, 2 .... , r (sufficient conditions, which in many cases are nearly necessary), or in terms of the existence of a positive-definite solution H of the Sylvester matrix algebraic equation e

Algebraic conditions for the absolute stability with probability 1 of the solutions of systems of linear stochastic ito equations with aftereffect. The case of a vector Wiener process and several delays

Algebraic conditions for the absolute stability with probability 1 of the solutions of systems of linear stochastic ito equations with aftereffect. The case of a vector Wiener process and several delays

ON STOCHASTIC EQUATIONS WITH DEGENERATE DIFFUSION WITH RESPECT TO SOME OF THE VARIABLES

In this paper the author establishes sufficient existence and uniqueness conditions for a strong solution of Ito's stochastic equation with nonsmooth drift under conditions of possible degeneracy of the diffusion with respect to some of the variables. The conditions thus found assume additional smoothness of the coefficients in the direction of the degeneracy. Bibliography: 13 titles.

Rotor Blade Stability in Turbulent Flows-Part I

The effect of turbulence in the atmosphere on the motion stability of a helicopter blade is investigated. Modeling turbulence as a random field, statistically stationary in time and homogeneous in space, the method of stochastic average of Stratonovich is used to obtain equivalent Ito stochastic equations, from which the FokkerPlanck equation for the transition probability density and the equations for various stochastic moments can be derived. As an exploratory study, only flapping and torsional motions are considered; the results are reported in two parts. In Part I, the present paper, equations of motion are derived which are reducible to those obtained previously by Sissingh and Kuczynski when the turbulence terms are removed. The in-plane turbulence components appear in the coefficients of these equations; thus, they affect the stability of the flapping and torsional motions. On the other hand, the normal turbulence component appears in the inhomogeneous terms in the equations; its statistical properties, while affecting the level of system response, do not change a stable solution to an unstable solution. Then detailed discussions are given for the reduced case of uncoupled flapping in a hovering flight. This simple case is theoretically interesting, since closed-form solutions can be obtained and considerable insight can be gained from the analysis. Certain mathematical tools involving stochastic processes which may be foreign to engineers are explained in the Appendix. Solutions for the case of forward flights for both coupled and uncoupled motions are presented in Part II.

Modelling and Adaptive Control of Urban Wastewater Treatment Plants

In this paper a Kinetic model for an activated sludge wastewater treatement plant based on the Monod single strain bacterial growth process is developed. In accounting for the unpredictable temporal variations in influent mass flow-rate and concentration, the consequent equations are shown to be nonlinear stochastic differential equations of the Ito type. Various effluent control strategies, including proportional and adaptive are investigated using a first order simulation algorithm for multivariable nonlinear stochastic Ito equations

Modelling a particular class of stochastic systems†

In this paper a method is given for obtaining a mathematical model of a class of black boxes having multiple inputs and multiple outputs in terms of Ito stochastic integral equations. This method is applicable to the class of black boxes having ergodic correlation functions when there is zero applied input. The point of view adopted in this paper is phenomenological in that it is desired that calculations made using the mathematical model should be 'close' to what is actually observed at the output of the black box.

On the uniqueness of the solution of a K. Ito's stochastic equation

The abstracts (in two languages) can be found in the pdf file of the article.
 Original author name(s) and title in Russian and Lithuanian:
 Д. Сургайлис. О единственности решения стохастического уравнения К. Ито
 D. Surgailis. Apie K. Ito stochastinės lygties sprendinio vienatinumą

The exponential stability and periodic solutions of Ito stochastic equations with small stochastic terms

The exponential stability and periodic solutions of Ito stochastic equations with small stochastic terms

The weak exponential stability and periodic solutions of Ito stochastic equations with small stochastic terms

The weak exponential stability and periodic solutions of Ito stochastic equations with small stochastic terms