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• W2040380081 abstract "Assuming that ${(X_n,Y_n)}$ is a sequence of cadlag processes converging in distribution to $(X,Y)$ in the Skorohod topology, conditions are given under which the sequence ${int X_n dY_n}$ converges in distribution to $int X dY$. Examples of applications are given drawn from statistics and filtering theory. In particular, assuming that $(U_n,Y_n) Rightarrow (U,Y)$ and that $F_n rightarrow F$ in an appropriate sense, conditions are given under which solutions of a sequence of stochastic differential equations $dX_n = dU_n + F_n(X_n)dY_n$ converge to a solution of $dX = dU + F(X)dY$, where $F_n$ and $F$ may depend on the past of the solution. As is well known from work of Wong and Zakai, this last conclusion fails if $Y$ is Brownian motion and the $Y_n$ are obtained by linear interpolation; however, the present theorem may be used to derive a generalization of the results of Wong and Zakai and their successors." @default.
• W2040380081 created "2016-06-24" @default.
• W2040380081 creator A5064447918 @default.
• W2040380081 creator A5065654526 @default.
• W2040380081 date "1991-07-01" @default.
• W2040380081 modified "2023-10-16" @default.
• W2040380081 title "Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations" @default.
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• W2040380081 doi "https://doi.org/10.1214/aop/1176990334" @default.
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