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

Dai Taguchi; Akihiro Tanaka

doi:10.1007/978-3-030-28535-7_9

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

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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 dX_t = σ(X_t)dW_t 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 dX_t = |X_t|^αdW_t, α ∈ (0, 1∕2) with non-sticky boundary condition and we give some remarks on CEV models in mathematical finance.

Original language	English
Title of host publication	Lecture Notes in Mathematics
Publisher	Springer
Pages	165-185
Number of pages	21
DOIs	https://doi.org/10.1007/978-3-030-28535-7_9
Publication status	Published - Jan 1 2019

Publication series

Name	Lecture Notes in Mathematics
Volume	2252
ISSN (Print)	0075-8434
ISSN (Electronic)	1617-9692

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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

Cite this

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

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Access to Document

10.1007/978-3-030-28535-7_9