Convergence at First and Second Order of Some Approximations of Stochastic Integrals

DOI10.1007/978-3-642-15217-7_10zbMath1218.60045OpenAlexW61285389MaRDI QIDQ3086802

Pierre Vallois, Blandine Bérard Bergery

Publication date: 30 March 2011

Published in: Séminaire de Probabilités XLIII (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-15217-7_10

zbMATH Keywords

regularizationstochastic integrationquadratic variationstochastic Fubini theoremfirst and second order convergence

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Martingales with continuous parameter (60G44) Stochastic integrals (60H05) Functional limit theorems; invariance principles (60F17) Local time and additive functionals (60J55)

Cites Work

• Convergence en loi des suites d'integrales stochastiques sur l'espace \({\mathbb{D}}^ 1\) de Skorokhod. (Convergence in law of sequences of stochastic integrals on the Skorokhod space \({\mathbb{D}}^ 1)\)
• Limit distributions for the error in approximations of stochastic integrals
• Approximation at first and second order of {\(m\)}-order integrals of the fractional {B}rownian motion and of certain semimartingales
• The generalized covariation process and Itô formula
• Ito formula for \(C^ 1\)-functions of semimartingales
• Central limit theorems for sequences of multiple stochastic integrals
• Stochastic calculus with respect to continuous finite quadratic variation processes
• Elements of Stochastic Calculus via Regularization
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