Approximation of Stochastic Volterra Equations with kernels of completely monotone type

by   Aurélien Alfonsi, et al.

In this work, we develop a multi-factor approximation for Stochastic Volterra Equations with Lipschitz coefficients and kernels of completely monotone type that may be singular. Our approach consists in truncating and then discretizing the integral defining the kernel, which corresponds to a classical Stochastic Differential Equation. We prove strong convergence results for this approximation. For the particular rough kernel case with Hurst parameter lying in (0,1/2), we propose various discretization procedures and give their precise rates of convergence. We illustrate the efficiency of our approximation schemes with numerical tests for the rough Bergomi model.


page 1

page 2

page 3

page 4


Semi-implicit Taylor schemes for stiff rough differential equations

We study a class of semi-implicit Taylor-type numerical methods that are...

Numerical methods for stochastic Volterra integral equations with weakly singular kernels

In this paper, we first establish the existence, uniqueness and Hölder c...

The BDF2-Maruyama Scheme for Stochastic Evolution Equations with Monotone Drift

We study the numerical approximation of stochastic evolution equations w...

Complete monotonicity-preserving numerical methods for time fractional ODEs

The time fractional ODEs are equivalent to the convolutional Volterra in...

Stochastic modified equations for symplectic methods applied to rough Hamiltonian systems based on the Wong--Zakai approximation

We investigate the stochastic modified equation which plays an important...

Analysis and approximation of some Shape-from-Shading models for non-Lambertian surfaces

The reconstruction of a 3D object or a scene is a classical inverse prob...

Efficient numerical evaluation of thermodynamic quantities on infinite (semi-)classical chains

This work presents an efficient numerical method to evaluate the free en...