On the Euler–Maruyama Scheme for Degenerate Stochastic Differential Equations with Non-sticky Condition

Dai Taguchi, Akihiro Tanaka

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

The aim of this paper is to study weak and strong convergence of the Euler–Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation dXt = σ(Xt)dWt with non-sticky condition. For proving this, we first prove that the Euler–Maruyama scheme also satisfies non-sticky condition. As an example, we consider stochastic differential equation dXt = |Xt|αdWt, α ∈ (0, 1∕2) with non-sticky boundary condition and we give some remarks on CEV models in mathematical finance.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer
Pages165-185
Number of pages21
DOIs
Publication statusPublished - 2019

Publication series

NameLecture Notes in Mathematics
Volume2252
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

Keywords

  • CEV models
  • Euler–Maruyama scheme
  • Hölder continuous diffusion coefficient
  • Mathematical finance
  • Non-sticky condition
  • Stochastic differential equations

ASJC Scopus subject areas

  • Algebra and Number Theory

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    Taguchi, D., & Tanaka, A. (2019). On the Euler–Maruyama Scheme for Degenerate Stochastic Differential Equations with Non-sticky Condition. In Lecture Notes in Mathematics (pp. 165-185). (Lecture Notes in Mathematics; Vol. 2252). Springer. https://doi.org/10.1007/978-3-030-28535-7_9