Positivity preserving truncated scheme for the stochastic Lotka–Volterra model with small moment convergence

Yongmei Cai, Qian Guo, Xuerong Mao

Research output: Journal PublicationArticlepeer-review

2 Citations (Scopus)

Abstract

This work concerns with the numerical approximation for the stochastic Lotka–Volterra model originally studied by Mao et al. (Stoch Process Appl 97(1):95–110, 2002). The natures of the model including multi-dimension, super-linearity of both the drift and diffusion coefficients and the positivity of the solution make most of the existing numerical methods fail. In particular, the super-linearity of the diffusion coefficient results in the explosion of the 1st moment of the analytical solution at a finite time. This becomes one of our main technical challenges. As a result, the convergence framework is to be set up under the θ
th moment with 0. The idea developed in this paper will not only be able to cope with the stochastic Lotka–Volterra model but also work for a large class of multi-dimensional super-linear SDE models.
Original languageEnglish
Article number24
JournalCalcolo
Volume60
DOIs
Publication statusPublished - 25 Apr 2023

Keywords

  • Stochastic differential equation
  • Positivity preserving numerical method
  • Multi-dimensional super-linear Lotka–Volterra model
  • Strong convergence

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

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