Weak consistency of the Euler method for numerically solving stochastic differential equations with discontinuous coefficients
We prove that, under appropriate conditions, the sequence of approximate solutions constructed according to the Euler scheme converges weakly to the (unique) solution of a stochastic differential equation with discontinuous coefficients. We also obtain a sufficient condition for the existence of a solution to a stochastic differential equation with discontinuous coefficients. These results are then applied to justify the technique of simulating continuous-time threshold autoregressive moving-average processes via the Euler scheme.
Year of publication: |
1998
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Authors: | Chan, K. S. ; Stramer, O. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 76.1998, 1, p. 33-44
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Publisher: |
Elsevier |
Keywords: | Good integrators Martingale differences Threshold ARMA processes |
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