On a one-parameter generalization of the Brownian bridge and associated quadratic functionals

DOI10.1007/s10959-004-0588-8zbMath1063.60049OpenAlexW2093517103MaRDI QIDQ1770908

Roger Mansuy

Publication date: 7 April 2005

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-004-0588-8

zbMATH Keywords

quadratic functionals\(\alpha\)-Brownian bridgemodified Bessel process

Mathematics Subject Classification ID

Gaussian processes (60G15) Brownian motion (60J65)

Related Items (16)

Asymptotic behaviours for maximum likelihood estimator of drift parameter in α-Wiener bridge process ⋮ Optimal Berry-Esséen bound for maximum likelihood estimation of the drift parameter in \(\alpha \)-Brownian bridge ⋮ Pinned diffusions and Markov bridges ⋮ Bias-correction of the maximum likelihood estimator for the \(\alpha\)-Brownian bridge ⋮ Existence and asymptotic behaviour of some time-inhomogeneous diffusions ⋮ Karhunen-Loève expansions of \(\alpha\)-Wiener bridges ⋮ When does allow the Hardy inequality to calculate an exact Poincaré constant on a line? ⋮ Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions ⋮ α-Wiener Bridges: Singularity of Induced Measures and Sample Path Properties ⋮ Operator scaled Wiener bridges ⋮ From an Itô type calculus for Gaussian processes to integrals of log-normal processes increasing in the convex order ⋮ Least squares estimator for \(\alpha\)-sub-fractional bridges ⋮ Bernstein processes, isovectors and mechanics ⋮ On the large deviation principle of generalized Brownian bridges ⋮ A Link Between Bougerol’s Identity and a Formula Due to Donati-Martin, Matsumoto and Yor ⋮ A family of interacting particle systems pinned to their ensemble average

Cites Work

• Conditioned stochastic differential equations: theory, examples and application to finance.
• Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions
• Bessel diffusions as a one-parameter family of diffusion processes
• Markov functions
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