Aspects of Brownian motion

DOI10.1007/978-3-540-49966-4zbMath1162.60022OpenAlexW1488346937MaRDI QIDQ946901

Marc Yor, Roger Mansuy

Publication date: 25 September 2008

Published in: Universitext (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-49966-4

zbMATH Keywords

Riemann zeta functionHilbert transformquadratic functionalsprincipal valuesDirichlet processexcursion theoryWalsh's Brownian motionAsian optionsconfluent hypergeometric functionsJacobi theta functionergodic propertytransfer principlewinding numbersspace-time harmonic functionsGaussian spaceBessel bridgesadditivity propertyBertoin's excursion theory for BES(d)beta and gamma variablesBiane's extensionsBismut's identityBrownian laceChung's identityCiesielski--Taylor identitiesconvolution of hitting timesFeynmann--Kac formulafiltration of Brownian bridgesfirst Wiener chaosFubini--Wiener integration by partsGauss linking numbergeneralized meandersHartman--Watson distributionKallianpur--Robbins ergodic theoremKnight's ratio formulaLévy--Khintchine representationLévy's arc sine lawLévy's area formulalocal time perturbation of Brownian motionOrnstein--Uhlenbeck processPetit's extensionsRay--Knight theoremsSpitzer's theoremYamada's formulae

Mathematics Subject Classification ID

Brownian motion (60J65) Other physical applications of random processes (60K40) Local time and additive functionals (60J55) Markov processes (60J99) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)

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