scholarly journals To the solution of the singular inhomogeneous integral Volterra equation

2017 ◽  
Vol 86 (2) ◽  
pp. 20-31
Author(s):  
T.N. Bekjan ◽  
◽  
M.T. Jenaliyev ◽  
S.A. Iskakov ◽  
M.I. Ramazanov ◽  
...  
Keyword(s):  
Volterra Equation ◽  
Integral Volterra Equation

scholarly journals Interpolation rational integral fraction of nth order on a continuum set of nodes

2021 ◽  
pp. 101-105
Author(s):  
Ihor Demkiv ◽  
Yaroslav Baranetskyi ◽  
Halyna Berehova
Keyword(s):  
Integral Equation ◽  
Volterra Equation ◽  
Standard Form ◽  
Integral Volterra Equation ◽  
Substitution Rule ◽  
Rational Integral

The paper constructs and investigates an integral rational interpolant of the nth order on a continuum set of nodes, which is the ratio of a functional polynomial of the first degree to a functional polynomial of the (n-1)th degree. Subintegral kernels are determined from the corresponding continuum conditions. Additionally, we obtain an integral equation to determine the kernel of the numerator integral. This integral equation, using elementary transformations, is reduced to the standard form of the integral Volterra equation of the second kind. Substituting the obtained solution into expressions for the rest of the kernels, we obtain expressions for all kernels included in the integral rational interpolant. Then, in order for a rational functional of the nth order to be interpolation on continuous nodes, it is sufficient for this functional to satisfy the substitution rule. Note that the resulting interpolant preserves any rational functional of the obtained form.

scholarly journals Continuous Dependence of the Solutions of Nonlinear Integral Quadratic Volterra Equation on the Parameter

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Szymon Dudek ◽  
Leszek Olszowy
Keyword(s):  
Banach Space ◽  
Hausdorff Distance ◽  
Continuous Dependence ◽  
Volterra Equation ◽  
Fréchet Space ◽  
Frechet Space ◽  
Integral Volterra Equation ◽  
Quadratic Integral ◽  
Continuous Dependence Of Solutions

We prove results on the existence and continuous dependence of solutions of a nonlinear quadratic integral Volterra equation on a parameter. This dependence is investigated in terms of Hausdorff distance. The considerations are placed in the Banach space and the Fréchet space.

LINEAR INTEGRAL VOLTERRA EQUATION OF THE FIRST KIND IN THE BANACH SPACE

2015 ◽  
Vol 4 (2) ◽  
pp. 8-13
Author(s):  
Зенина ◽  
V. Zenina ◽  
Сапронов ◽  
Ivan Sapronov ◽  
Уточкина ◽  
...  
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Volterra Integral Equation ◽  
Volterra Equation ◽  
Polynomial Kernel ◽  
Integral Volterra Equation ◽  
Integrable Functions ◽  
Linear Integral ◽  
Space Of Integrable Functions

We construct solutions to a singular Volterra integral equation of the first kind with а polynomial kernel in the space of integrable functions whose values be-long to a Banach space.

scholarly journals Self-exciting multifractional processes

2021 ◽  
Vol 58 (1) ◽  
pp. 22-41
Author(s):  
Fabian A. Harang ◽  
Marc Lagunas-Merino ◽  
Salvador Ortiz-Latorre
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Rate Of Convergence ◽  
Existence And Uniqueness ◽  
Volterra Equation ◽  
The Self ◽  
The Past ◽  
Stochastic Volterra Equation ◽  
Multifractional Brownian Motion ◽  
Self Organizing

AbstractWe propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this by means of a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as giving bounds on the p-order moments, for all $p\geq1$. We show convergence of an Euler–Maruyama scheme for the process, and also give the rate of convergence, which is dependent on the self-exciting dynamics of the process. Moreover, we discuss various applications of this process, and give examples of different functions to model self-exciting behavior.

scholarly journals Existence for a doubly nonlinear Volterra equation

2007 ◽  
Vol 333 (2) ◽  
pp. 839-862 ◽  
Author(s):  
Gianni Gilardi ◽  
Ulisse Stefanelli
Keyword(s):  
Volterra Equation ◽  
Doubly Nonlinear
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