Itô’s Formula and Applications

Mircea Grigoriu ()
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Mircea Grigoriu: Cornell University

Chapter Chapter 5 in Stochastic Systems, 2012, pp 155-199 from Springer

Abstract: Abstract Itô’s formula is establish for real-valued and $${\mathbb{R}}^d$$ -valued continuous and arbitrary semimartingales and its use is illustrated by numerous examples. The relationship between the Itô and Stratonovich integrals is examined prior to presenting a broad range of applications of Itô’s formula. The applications include stochastic differential equations with Gaussian and non-Gaussian white noise, Tanaka’s formula, local solutions for a class of partial differential equations, and improved Monte Carlo estimates based on Girsanov’s theorem.

Keywords: Brownian Motion; Stochastic Differential Equation; Strong Solution; Variable Formula; Colored Noise (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:ssrchp:978-1-4471-2327-9_5

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DOI: 10.1007/978-1-4471-2327-9_5

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