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1999•The Annals of Applied ProbabilityOpen access

Stochastic calculus for Brownian motion on a Brownian fracture

Davar Khoshnevisan, Thomas M. Lewis

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Abstract

In this paper, we give a pathwise development of stochastic integrals with respect to iterated Brownian motion. We also provide a detailed analysis of the variations of iterated Brownian motion. These variations are linked to Brownian motion in random scenery and iterated Brownian motion itself.

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What this paper is about

In this paper, we give a pathwise development of stochastic integrals with respect to iterated Brownian motion. We also provide a detailed analysis of the variations of iterated Brownian motion. These variations are linked to Brownian motion in random scenery and iterated Brownian motion itself.

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OpenAlex reports 40 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we give a pathwise development of stochastic integrals with respect to iterated Brownian motion. We also provide a detailed analysis of the variations of iterated Brownian motion. These variations are linked to Brownian motion in random scenery and iterated Brownian motion itself.

Key concepts: Mathematics, Geometric Brownian motion, Iterated function, Brownian motion, Diffusion process, Reflected Brownian motion, Brownian excursion, Martingale representation theorem

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