On the existence of a random solution to a nonlinear perturbed stochastic integral equation

1976 ◽  
Vol 28 (1) ◽  
pp. 99-109 ◽  
Author(s):  
A. N. V. Rao ◽  
Chris P. Tsokos
Keyword(s):  
Integral Equation ◽  
Stochastic Integral ◽  
Random Solution ◽  
Stochastic Integral Equation

The method of V. M. Popov for differential systems with random parameters

1971 ◽  
Vol 8 (2) ◽  
pp. 298-310 ◽  
Author(s):  
Chris P. Tsokos
Keyword(s):  
Integral Equation ◽  
Frequency Response ◽  
Absolute Stability ◽  
Stochastic Integral ◽  
Random Parameters ◽  
Random Solution ◽  
Stochastic Integral Equation ◽  
Differential Systems ◽  
Frequency Response Method ◽  
Response Method

The aim of this paper is to investigate the existence of a random solution and the stochastic absolute stability of the differential systems (1.0)–(1.1) and (1.2)–(1.3) with random parameters. These objectives are accomplished by reducing the differential systems into a stochastic integral equation of the convolution type of the form (1.4) and utilizing a generalized version of V. M. Popov's frequency response method.

Stochastic asymptotic exponential stability of stochastic integral equations

1972 ◽  
Vol 9 (01) ◽  
pp. 169-177
Author(s):  
Chris P. Tsokos ◽  
M. A. Hamdan
Keyword(s):  
Integral Equation ◽  
Exponential Stability ◽  
Stochastic Integral ◽  
Stability Theorem ◽  
Random Solution ◽  
Stochastic Integral Equation ◽  
Classical Stability ◽  
Stochastic Integral Equations ◽  
Exponentially Stable ◽  
Image Position

The object of this paper is to study the stochastic asymptotic exponential stability of a stochastic integral equation of the form A random solution of the stochastic integral equation is considered to be a second order stochastic process satisfying the equation almost surely. The random solution, y(t, ω) is said to be. stochastically asymptotically exponentially stable if there exist some β > 0 and a γ > 0 such that for t∈ R +. The results of the paper extend the results of Tsokos' generalization of the classical stability theorem of Poincaré-Lyapunov.

scholarly journals On a random solution of a nonlinear perturbed stochastic integral equation of the Volterra type

1973 ◽  
Vol 9 (2) ◽  
pp. 227-237 ◽  
Author(s):  
J. Susan Milton ◽  
Chris P. Tsokos
Keyword(s):  
Integral Equation ◽  
Stochastic Integral ◽  
Random Variable ◽  
Random Solution ◽  
Stochastic Integral Equation ◽  
Almost Everywhere ◽  
Image Position ◽  
Probability Measure Space ◽  
Complete Probability ◽  
Vector Random Variable

The object of this present paper is to study a nonlinear perturbed stochastic integral equation of the formwhere ω ∈ Ω, the supporting set of the complete probability measure space (Ω A, μ). We are concerned with the existence and uniqueness of a random solution to the above equation. A random solution, x(t; ω), of the above equation is defined to be a vector random variable which satisfies the equation μ almost everywhere.

Stochastic asymptotic exponential stability of stochastic integral equations

1972 ◽  
Vol 9 (1) ◽  
pp. 169-177 ◽  
Author(s):  
Chris P. Tsokos ◽  
M. A. Hamdan
Keyword(s):  
Integral Equation ◽  
Exponential Stability ◽  
Stochastic Integral ◽  
Stability Theorem ◽  
Random Solution ◽  
Stochastic Integral Equation ◽  
Classical Stability ◽  
Stochastic Integral Equations ◽  
Exponentially Stable ◽  
Image Position

The object of this paper is to study the stochastic asymptotic exponential stability of a stochastic integral equation of the form A random solution of the stochastic integral equation is considered to be a second order stochastic process satisfying the equation almost surely. The random solution, y(t, ω) is said to be. stochastically asymptotically exponentially stable if there exist some β > 0 and a γ > 0 such that for t∈ R+.The results of the paper extend the results of Tsokos' generalization of the classical stability theorem of Poincaré-Lyapunov.

The method of V. M. Popov for differential systems with random parameters

1971 ◽  
Vol 8 (02) ◽  
pp. 298-310
Author(s):  
Chris P. Tsokos
Keyword(s):  
Integral Equation ◽  
Frequency Response ◽  
Absolute Stability ◽  
Stochastic Integral ◽  
Random Parameters ◽  
Random Solution ◽  
Stochastic Integral Equation ◽  
Differential Systems ◽  
Frequency Response Method ◽  
Response Method

The aim of this paper is to investigate the existence of a random solution and the stochastic absolute stability of the differential systems (1.0)–(1.1) and (1.2)–(1.3) with random parameters. These objectives are accomplished by reducing the differential systems into a stochastic integral equation of the convolution type of the form (1.4) and utilizing a generalized version of V. M. Popov's frequency response method.

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