TY - JOUR
T1 - Product expansion for stochastic jump diffusions and its application to numerical approximation
AU - Liu, X. Q.
AU - Li, C. W.
PY - 1999/8/15
Y1 - 1999/8/15
N2 - We derive a product expansion of the exponential Lie series in terms of a Philip Hall basis for the Chen series corresponding to the stochastic jump diffusion as in Sussmann (in: C.I. Byrnes and A. Lindquist (Eds.), Theory and Applications of Nonlinear Control Systems, North-Holland, Amsterdam, 1986, pp. 323-335) for the deterministic case. Based on the expansion, we establish the Stratonovich-Taylor-Hall (STH) schemes such that each scheme involves only the minimum number of multiple stochastic integrals, which can be regarded as systems of stochastic differential equations and approximated by a lower order scheme with an appropriate step size to ensure the necessary accuracy. Mean-square convergence of the STH schemes is shown and numerical examples are provided to illustrate the results. © 1999 Elsevier Science B.V.
AB - We derive a product expansion of the exponential Lie series in terms of a Philip Hall basis for the Chen series corresponding to the stochastic jump diffusion as in Sussmann (in: C.I. Byrnes and A. Lindquist (Eds.), Theory and Applications of Nonlinear Control Systems, North-Holland, Amsterdam, 1986, pp. 323-335) for the deterministic case. Based on the expansion, we establish the Stratonovich-Taylor-Hall (STH) schemes such that each scheme involves only the minimum number of multiple stochastic integrals, which can be regarded as systems of stochastic differential equations and approximated by a lower order scheme with an appropriate step size to ensure the necessary accuracy. Mean-square convergence of the STH schemes is shown and numerical examples are provided to illustrate the results. © 1999 Elsevier Science B.V.
KW - 41A58
KW - 60G55
KW - 60J65
KW - Exponential Lie series
KW - Jump diffusion
KW - Mean square convergence
KW - Multiple stochastic integral Stratonovich-Taylor expansion
KW - Philip Hall basis Shuffle product
KW - Primary 65U05
KW - Secondary 60H10
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0032599425&origin=recordpage
U2 - 10.1016/S0377-0427(99)00095-3
DO - 10.1016/S0377-0427(99)00095-3
M3 - RGC 21 - Publication in refereed journal
SN - 0377-0427
VL - 108
SP - 1
EP - 17
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1-2
ER -