The Annals of Probability

Convergence in various topologies for stochastic integrals driven by semimartingales

Adam Jakubowski

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We generalize existing limit theory for stochastic integrals driven by semimartingales and with left-continuous integrands. Joint Skorohod convergence is replaced with joint finite dimensional convergence plus an assumption excluding the case when oscillations of the integrand appear immediately before oscillations of the integrator. Integrands may converge in a very weak topology. It is also proved that convergence of integrators implies convergence of stochastic integrals with respect to the same topology.

Article information

Ann. Probab., Volume 24, Number 4 (1996), 2141-2153.

First available in Project Euclid: 6 January 2003

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Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60H05: Stochastic integrals 60B10: Convergence of probability measures

Stochastic integral Skorohod topology functional convergence semimartingales


Jakubowski, Adam. Convergence in various topologies for stochastic integrals driven by semimartingales. Ann. Probab. 24 (1996), no. 4, 2141--2153. doi:10.1214/aop/1041903222.

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