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Stability in \(\mathbb D\) of martingales and backward equations under discretization of filtration. (English) Zbl 0932.60047
Let \(Y^n\) be the step processes defined by discretization in time of a càdlàg process \(Y\) and let \((\mathcal F ^n_t)\) and \((\mathcal F_t)\) be the respective filtrations generated by \(Y^n\) and \(Y\). Stability in \(\mathbb D\) (with Skorokhod topology) of \((\mathcal F^n_t)\)-martingales and of \((\mathcal F^n_t)\)-solutions of corresponding backward equations are studied as \(Y^n\to Y\). The stability of the martingales is proved if \(Y\) is a Markov process; in a more general case it may fail. The solutions of the backward equations are shown to converge in law or in probability under suitable sets of assumptions.

60G44 Martingales with continuous parameter
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
Full Text: DOI
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