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October 1996 Convergence in various topologies for stochastic integrals driven by semimartingales
Adam Jakubowski
Ann. Probab. 24(4): 2141-2153 (October 1996). DOI: 10.1214/aop/1041903222

Abstract

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.

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Adam Jakubowski. "Convergence in various topologies for stochastic integrals driven by semimartingales." Ann. Probab. 24 (4) 2141 - 2153, October 1996. https://doi.org/10.1214/aop/1041903222

Information

Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0871.60028
MathSciNet: MR1415245
Digital Object Identifier: 10.1214/aop/1041903222

Subjects:
Primary: 60F17
Secondary: 60B10 , 60H05

Keywords: Functional convergence , Semimartingales , Skorohod topology , stochastic integral

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 4 • October 1996
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