On a stochastic integral equation of the Volterra type

1969 ◽  
Vol 3 (3) ◽  
pp. 222-231 ◽  
Author(s):  
Chris P. Tsokos
Keyword(s):  
Integral Equation ◽  
Stochastic Integral ◽  
Volterra Type ◽  
Stochastic Integral Equation

On solutions of a stochastic integral equation of the volterra type with applications for chemotherapy

1988 ◽  
Vol 25 (02) ◽  
pp. 257-267 ◽  
Author(s):  
D. Szynal ◽  
S. Wedrychowicz
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Stochastic Model ◽  
Asymptotic Behaviour ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Volterra Type ◽  
Stochastic Integral Equation

This paper deals with the existence of solutions of a stochastic integral equation of the Volterra type and their asymptotic behaviour. Investigations of this paper use the concept of a measure of non-compactness in Banach space and fixed-point theorem of Darbo type. An application to a stochastic model for chemotherapy is also presented.

On a stochastic integral equation of the Volterra type in telephone traffic theory

1971 ◽  
Vol 8 (02) ◽  
pp. 269-275 ◽  
Author(s):  
W. J. Padgett ◽  
C. P. Tsokos
Keyword(s):  
Integral Equation ◽  
Stochastic Integral ◽  
Random Variable ◽  
Scalar Function ◽  
List Type ◽  
Volterra Type ◽  
Stochastic Integral Equation ◽  
Image Position ◽  
Traffic Theory ◽  
Telephone Traffic

In mathematical models of phenomena occurring in the general areas of the engineering, biological, and physical sciences, random or stochastic equations appear frequently. In this paper we shall formulate a problem in telephone traffic theory which leads to a stochastic integral equation which is a special case of the Volterra type of the form where: (i) ω∊Ω, where Ω is the supporting set of the probability measure space (Ω,B,P); (ii) x(t; ω) is the unknown random variable for t ∊ R +, where R + = [0, ∞); (iii) y(t; ω) is the stochastic free term or free random variable for t ∊ R +; (iv) k(t, τ; ω) is the stochastic kernel, defined for 0 ≦ τ ≦ t < ∞; and (v) f(t, x) is a scalar function defined for t ∊ R + and x ∊ R, where R is the real line.

scholarly journals Existence of solutions of a class of stochastic Volterra integral equations with applications to chemotherapy

1999 ◽  
Vol 41 (1) ◽  
pp. 93-104 ◽  
Author(s):  
R. Subramaniam ◽  
K. Balachandran
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Stochastic Model ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Volterra Type ◽  
Stochastic Integral Equation ◽  
The Fixed Point Theorem

AbstractIn this paper we establish the existence of solutions of a more general class of stochastic integral equation of Volterra type. The main tools used here are the measure of noncompactness and the fixed point theorem of Darbo. The results generalize the results of Tsokos and Padgett [9] and Szynal and Wedrychowicz [7]. An application to a stochastic model arising in chemotherapy is discussed.

On solutions of a stochastic integral equation of the volterra type with applications for chemotherapy

1988 ◽  
Vol 25 (2) ◽  
pp. 257-267 ◽  
Author(s):  
D. Szynal ◽  
S. Wedrychowicz
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Stochastic Model ◽  
Asymptotic Behaviour ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Volterra Type ◽  
Stochastic Integral Equation

This paper deals with the existence of solutions of a stochastic integral equation of the Volterra type and their asymptotic behaviour. Investigations of this paper use the concept of a measure of non-compactness in Banach space and fixed-point theorem of Darbo type. An application to a stochastic model for chemotherapy is also presented.

On a stochastic integral equation of the Volterra type in telephone traffic theory

1971 ◽  
Vol 8 (2) ◽  
pp. 269-275 ◽  
Author(s):  
W. J. Padgett ◽  
C. P. Tsokos
Keyword(s):  
Integral Equation ◽  
Stochastic Integral ◽  
Random Variable ◽  
Scalar Function ◽  
List Type ◽  
Volterra Type ◽  
Stochastic Integral Equation ◽  
Image Position ◽  
Traffic Theory ◽  
Telephone Traffic

In mathematical models of phenomena occurring in the general areas of the engineering, biological, and physical sciences, random or stochastic equations appear frequently. In this paper we shall formulate a problem in telephone traffic theory which leads to a stochastic integral equation which is a special case of the Volterra type of the form where: (i)ω∊Ω, where Ω is the supporting set of the probability measure space (Ω,B,P);(ii)x(t; ω) is the unknown random variable for t ∊ R+, where R+ = [0, ∞);(iii)y(t; ω) is the stochastic free term or free random variable for t ∊ R+;(iv)k(t, τ; ω) is the stochastic kernel, defined for 0 ≦ τ ≦ t < ∞; and(v)f(t, x) is a scalar function defined for t ∊ R+ and x ∊ R, where R is the real line.

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