TY - JOUR
T1 - A General Framework to Simulate Diffusions with Discontinuous Coefficients and Local Times
AU - Ding, Kailin
AU - Cui, Zhenyu
N1 - Publisher Copyright:
© 2022 Copyright held by the owner/author(s). Publication rights licensed to ACM.
PY - 2022/11/5
Y1 - 2022/11/5
N2 - In this article, we propose an efficient general simulation method for diffusions that are solutions to stochastic differential equations with discontinuous coefficients and local time terms. The proposed method is based on sampling from the corresponding continuous-time Markov chain approximation. In contrast to existing time discretization schemes, the Markov chain approximation method corresponds to a spatial discretization scheme and is demonstrated to be particularly suited for simulating diffusion processes with discontinuities in their state space. We establish the theoretical convergence order and also demonstrate the accuracy and robustness of the method in numerical examples by comparing it to the known benchmarks in terms of root mean squared error, runtime, and the parameter sensitivity.
AB - In this article, we propose an efficient general simulation method for diffusions that are solutions to stochastic differential equations with discontinuous coefficients and local time terms. The proposed method is based on sampling from the corresponding continuous-time Markov chain approximation. In contrast to existing time discretization schemes, the Markov chain approximation method corresponds to a spatial discretization scheme and is demonstrated to be particularly suited for simulating diffusion processes with discontinuities in their state space. We establish the theoretical convergence order and also demonstrate the accuracy and robustness of the method in numerical examples by comparing it to the known benchmarks in terms of root mean squared error, runtime, and the parameter sensitivity.
KW - CTMC approximation
KW - Diffusion
KW - discontinuous coefficient
KW - local time
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U2 - 10.1145/3559541
DO - 10.1145/3559541
M3 - Article
AN - SCOPUS:85149174854
SN - 1049-3301
VL - 32
JO - ACM Transactions on Modeling and Computer Simulation
JF - ACM Transactions on Modeling and Computer Simulation
IS - 4
M1 - 22
ER -