Decomposing the Brownian path via the range process

DOI10.1016/0304-4149(94)00044-TzbMath0820.60063MaRDI QIDQ1346156

Pierre Vallois

Publication date: 31 August 1995

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

Brownian motionmartingalesrange process

Mathematics Subject Classification ID

Brownian motion (60J65) Stopping times; optimal stopping problems; gambling theory (60G40) Martingales with continuous parameter (60G44) Sample path properties (60G17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Markov processes (60J99)

Related Items

Range of Brownian motion with drift, Product of two multiple stochastic integrals with respect to a normal martingale, On distributions of integral functionals of diffusions stopped at inverse range time, Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions, Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians, On first range times of linear diffusions, Random Brownian scaling identities and splicing of Bessel processes

Cites Work

• The concave majorant of Brownian motion
• On the range of Brownian motion and its inverse process
• A construction of the Brownian path from \(\mathbf{BES}^ 3\) pieces
• Exit systems
• Diffusion arrêtée au premier instant où l'amplitude atteint un niveau donné
• The Asymptotic Distribution of the Range of Sums of Independent Random Variables
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