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January 2020 Itô’s formula for Gaussian processes with stochastic discontinuities
Christian Bender
Ann. Probab. 48(1): 458-492 (January 2020). DOI: 10.1214/19-AOP1369

Abstract

We introduce a Skorokhod type integral and prove an Itô formula for a wide class of Gaussian processes which may exhibit stochastic discontinuities. Our Itô formula unifies and extends the classical one for general (i.e., possibly discontinuous) Gaussian martingales in the sense of Itô integration and the one for stochastically continuous Gaussian non-martingales in the Skorokhod sense, which was first derived in Alòs et al. (Ann. Probab. 29 (2001) 766–801).

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Christian Bender. "Itô’s formula for Gaussian processes with stochastic discontinuities." Ann. Probab. 48 (1) 458 - 492, January 2020. https://doi.org/10.1214/19-AOP1369

Information

Received: 1 November 2017; Revised: 1 December 2018; Published: January 2020
First available in Project Euclid: 25 March 2020

zbMATH: 07206765
MathSciNet: MR4079443
Digital Object Identifier: 10.1214/19-AOP1369

Subjects:
Primary: 60G15, 60H05, 60H07

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • January 2020
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