Approximate solution of the integral equations involving kernel with additional singularity
Анотація
The article is devoted to the approximate solutions of the Fredholm integral equations of the second kind with the weak singular kernel that can have additional singularity in the numerator. We describe two problems that lead to such equations. They are the problem of minimization of small deviations and the entropy minimization problem. Both of them appear when considering a dynamical system involving a mixed fractional Brownian motion. In order to apply well-known numerical methods for weakly singular kernels, we build the continuous approximation of the solution of an integral equation with the kernel containing additional singularity by the solutions of the integral equations whose kernels are weakly singular, but the numerator is continuous. We prove that the approximated solutions tend to the solution of the original equation. We demonstrate numerically how our methods work being applied to our specific integral equations.
Класифікація
Ідентифікатори
Рецензії (0)
Написати рецензіюРецензій ще немає. Будьте першим!
Схожі роботи
Fractional stochastic heat equation with piecewise constant coefficients
Схоже за: Stochastic processes and financial applications · Fractional Differential Equations Solutions · Complex Systems and Time Series Analysis
Maximum Likelihood Drift Estimation for the Mixing of Two Fractional Brownian Motions
Схоже за: Stochastic processes and financial applications · Complex Systems and Time Series Analysis
Approximation of multifractional Brownian motion by absolutely continuous processes
Схоже за: Stochastic processes and financial applications · Complex Systems and Time Series Analysis
Drift Parameter Estimation in Diffusion and Fractional Diffusion Models
Схоже за: Stochastic processes and financial applications · Fractional Differential Equations Solutions
Asymptotic Growth of Sample Paths of Tempered Fractional Brownian Motions, with Statistical Applications to Vasicek-Type Models
Схоже за: Stochastic processes and financial applications · Complex Systems and Time Series Analysis
Path Space Large Deviations of a Large Buffer with Gaussian Input Traffic
Схоже за: Stochastic processes and financial applications · Complex Systems and Time Series Analysis