Stochastic Volterra integral equations with doubly singular kernels and their numerical solutions

DOI10.1016/j.cnsns.2022.106796OpenAlexW4290860718WikidataQ114196383 ScholiaQ114196383MaRDI QIDQ2094415

Min Li

Publication date: 28 October 2022

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2022.106796

zbMATH Keywords

strong convergence rateMilstein-type schemesum-of-exponentials approximationmultilevel Monte Carlo techniquestochastic Volterra integral equations with doubly singular kernels

Mathematics Subject Classification ID

Stochastic analysis (60Hxx) Singular integral equations (45Exx) Probabilistic methods, stochastic differential equations (65Cxx)

Cites Work

• Strong superconvergence of the Euler-Maruyama method for linear stochastic Volterra integral equations
• Improved rectangular method on stochastic Volterra equations
• Numerical solution of two-dimensional weakly singular stochastic integral equations on non-rectangular domains via radial basis functions
• Integral equations with diagonal and boundary singularities of the kernel
• Euler schemes and large deviations for stochastic Volterra equations with singular kernels
• Existence and uniqueness of solutions to stochastic Volterra equations with singular kernels and non-Lipschitz coefficients
• Geometric theory of semilinear parabolic equations
• Split-step collocation methods for stochastic Volterra integral equations
• Approximation schemes for Itô-Volterra stochastic equations
• Lévy-driven stochastic Volterra integral equations with doubly singular kernels: existence, uniqueness, and a fast EM method
• A two-parameter Milstein method for stochastic Volterra integral equations
• Euler-Maruyama scheme for Caputo stochastic fractional differential equations
• Mean-square stability and convergence of a split-step theta method for stochastic Volterra integral equations
• Improved \(\vartheta\)-methods for stochastic Volterra integral equations
• Asymptotic separation for stochastic Volterra integral equations with doubly singular kernels
• Discrete-time simulation of stochastic Volterra equations
• Numerical solution of stochastic Itô-Volterra integral equation by using shifted Jacobi operational matrix method
• Convergence analysis of an iterative numerical algorithm for solving nonlinear stochastic Itô-Volterra integral equations with \(m\)-dimensional Brownian motion
• Nash equilibrium approximation of some class of stochastic differential games: a combined Chebyshev spectral collocation method with policy iteration
• Multilevel Monte Carlo Path Simulation
• NUMERICAL SOLUTION OF VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNELS WHICH MAY HAVE A BOUNDARY SINGULARITY
• Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
• Multifactor Approximation of Rough Volatility Models

This page was built for publication: Stochastic Volterra integral equations with doubly singular kernels and their numerical solutions