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 -