The Annals of Applied Probability

Stochastic calculus for Brownian motion on a Brownian fracture

Davar Khoshnevisan and Thomas M. Lewis

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 3 (1999), 629-667.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962807

Digital Object Identifier
doi:10.1214/aoap/1029962807

Mathematical Reviews number (MathSciNet)
MR1722276

Zentralblatt MATH identifier
0956.60054

Subjects
Primary: 60H05: Stochastic integrals
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx] 60F12

Keywords
Iterated Brownian motion Brownian motion in random scenery stochastic integration sample-path variations excursion theory

Citation

Khoshnevisan, Davar; Lewis, Thomas M. Stochastic calculus for Brownian motion on a Brownian fracture. Ann. Appl. Probab. 9 (1999), no. 3, 629--667. doi:10.1214/aoap/1029962807. https://projecteuclid.org/euclid.aoap/1029962807


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  • SALT LAKE CITY, UTAH 84112 GREENVILLE, SOUTH CAROLINA 29613 E-MAIL: davar@math.utah.edu E-MAIL: tom.lewis@furman.edu