TY - CHAP

T1 - On the Euler–Maruyama Scheme for Degenerate Stochastic Differential Equations with Non-sticky Condition

AU - Taguchi, Dai

AU - Tanaka, Akihiro

N1 - Funding Information:
Acknowledgements The authors would like to thank Professor Masatoshi Fukushima for his valuable comments. The authors would also like to thank an anonymous referee for his/her careful readings and advices. The first author was supported by JSPS KAKENHI Grant Number 17H06833. The second author was supported by Sumitomo Mitsui Banking Corporation.
Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - CEV models

KW - Euler–Maruyama scheme

KW - Hölder continuous diffusion coefficient

KW - Mathematical finance

KW - Non-sticky condition

KW - Stochastic differential equations

UR - http://www.scopus.com/inward/record.url?scp=85075906110&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075906110&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-28535-7_9

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

M3 - Chapter

AN - SCOPUS:85075906110

T3 - Lecture Notes in Mathematics

SP - 165

EP - 185

BT - Lecture Notes in Mathematics

PB - Springer

ER -