RESEARCH IN PAIRSg-Measures: Uniqueness and Properties (event 2112)Dates: Place: CIRM (Marseille Luminy, France) |

DESCRIPTION |
PARTICIPANTS |

BackgroundAn interesting problem in probability theory was introduced by Keane in 1972 and formulated in terms of what he called g-measures. Their definition can be formulated in terms of the jacobian (which is function and denoted by the g in question) of the measure and the requirement that it is continuous. A basic problem is to determine what stronger properties of the jacobian are required to show that there is associated a unique g-measure. A particularly fruitful approach is using transfer operators. A major breakthrough some years ago was when Oberg and Johansson used a martingale argument to give a criterion for uniqueness. Since then, there has been steady progress in obtaining optimal hypotheses for uniqueness of the g-measure. AimsWe would like to explore the delicate question of the threshold conditions for the uniqueness of the g-measures. This is expressed in terms of the regularity of the function g, usually expressed in terms of the variations of the function. Pollicott, Johansson (Gavle) and Oberg (Uppsala) have a long standing collaboration on this project which has already resulted in substantial progress. |
Anders Johansson (Högskolan i Gävle University)Anders Öberg (Uppsala University)Mark Pollicott (University of Warwick)Anthony Quas (University of Victoria)Sandro Vaienti (CPT & Université de Toulon) |

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