A version of Pitman's 2M — X theorem for geometric Brownian motions

DOI10.1016/S0764-4442(99)80326-7zbMath0936.60076OpenAlexW2078846859MaRDI QIDQ4260077

Marc Yor, Hiroyuki Matsumoto

Publication date: 9 May 2000

Published in: Comptes Rendus de l'Académie des Sciences - Series I - Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0764-4442(99)80326-7

zbMATH Keywords

geometric Brownian motionthree-dimensional Bessel processgeneralized inverse Gaussian distributionsRogers-Pitman extension

Mathematics Subject Classification ID

Brownian motion (60J65) Diffusion processes (60J60)

Related Items (15)

Discrete integrable systems and Pitman's transformation ⋮ Yang-Baxter maps and independence preserving property ⋮ Directed polymers and the quantum Toda lattice ⋮ Exponential functionals of Brownian motion and class-one Whittaker functions ⋮ Tropical combinatorics and Whittaker functions ⋮ Interpretation via Brownian motion of some independence properties between GIG and gamma variables. ⋮ Geometric RSK and the Toda lattice ⋮ An Analogue of Pitman’s 2M — X Theorem for Exponential Wiener Functionals Part II: The Role of the Generalized Inverse Gaussian Laws ⋮ Brownian analogues of Burke's theorem. ⋮ Stochastic Bäcklund Transformations ⋮ Matsumoto–Yor Process and Infinite Dimensional Hyperbolic Space ⋮ Tree structured independence for exponential Brownian functionals ⋮ Interacting diffusions on positive definite matrices ⋮ Bi-infinite solutions for KdV- and Toda-type discrete integrable systems based on path encodings ⋮ Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions.

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