Harnesses, Lévy bridges and Monsieur Jourdain

DOI10.1016/j.spa.2004.09.001zbMath1070.60041arXivmath/0406563OpenAlexW2093967571MaRDI QIDQ2485829

Roger Mansuy, Marc Yor

Publication date: 5 August 2005

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

Full work available at URL: https://arxiv.org/abs/math/0406563

zbMATH Keywords

Lévy processesEnlargement of filtrationPast-future martingales

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stationary stochastic processes (60G10) Generalizations of martingales (60G48) Martingales with continuous parameter (60G44)

Related Items (19)

Approximation and simulation of infinite-dimensional Lévy processes ⋮ Flows in near algebras with applications to harnesses ⋮ On Markov processes with polynomial conditional moments ⋮ A characterisation of the Gaussian free field ⋮ The stochastic Leibniz formula for Volterra integrals under enlarged filtrations ⋮ Generalized stationary random fields with linear regressions - an operator approach ⋮ A new CLT for additive functionals of Markov chains ⋮ Stitching pairs of Lévy processes into harnesses ⋮ Generalised liouville processes and their properties ⋮ Zonal polynomials and a multidimensional quantum Bessel process ⋮ Quadratic harnesses, $q$-commutations, and orthogonal martingale polynomials ⋮ Askey-Wilson polynomials, quadratic harnesses and martingales ⋮ Markov processes on time-like graphs ⋮ Pricing electricity forwards under future information on the stochastic mean-reversion level ⋮ The classical bi-Poisson process: an invertible quadratic harness ⋮ Wilson's $6-j$ Laws and Stitched Markov Processes ⋮ Optimal insider control and semimartingale decompositions under enlargement of filtration ⋮ An anticipative stochastic minimum principle under enlarged filtrations ⋮ Conditioned point processes with application to Lévy bridges

Cites Work

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• Harness processes and harmonic crystals
• Time reversal on Lévy processes
• Tails in harnesses
• A parallel between Brownian bridges and gamma bridges
• Kendall's identity for the first crossing time revisited
• The serial harness interacting with a wall
• Un théorème d'invariance projective relatif au mouvement brownien
• Two-parameter harnesses and the Wiener process
• Properties of Large Eden Clusters in the Plane
• Exercises in Probability
• Optimal portfolio for an insider in a market driven by Lévy processes§

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