DeepAI AI Chat
Log In Sign Up

Lamperti Semi-Discrete method

04/13/2021
by   N. Halidias, et al.
0

We study the numerical approximation of numerous processes, solutions of nonlinear stochastic differential equations, that appear in various applications such as financial mathematics and population dynamics. Between the investigated models are the CIR process, also known as the square root process, the constant elasticity of variance process CEV, the Heston 3/2-model, the Aït-Sahalia model and the Wright-Fisher model. We propose a version of the semi-discrete method, which we call Lamperti semi-discrete (LSD) method. The LSD method is domain preserving and seems to converge strongly to the solution process with order 1 and no extra restrictions on the parameters or the step-size.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/21/2020

Convergence rates of the Semi-Discrete method for stochastic differential equations

We study the convergence rates of the semi-discrete (SD) method original...
08/06/2020

A note on the asymptotic stability of the Semi-Discrete method for Stochastic Differential Equations

We study the asymptotic stability of the semi-discrete (SD) numerical me...
07/26/2023

Domain preserving and strongly converging explicit scheme for the stochastic SIS epidemic model

In this article, we construct a numerical method for a stochastic versio...
09/03/2019

High order discretization methods for spatial dependent SIR models

In this paper, an SIR model with spatial dependence is studied, and resu...
01/22/2021

Numerical Methods for Backward Stochastic Differential Equations: A Survey

Backwards Stochastic Differential Equations (BSDEs) have been widely emp...