{"http:\/\/dx.doi.org\/10.14288\/1.0376735":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Non UBC","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Merlev\u00e8de, Florence","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2019-03-11T08:36:28Z","type":"literal","lang":"en"},{"value":"2017-05-30T09:48","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"his talk is devoted to strong approximations in the dependent setting. The famous results of Koml\\'os, Major and Tusn\\'ady (1975-1976)  state that it\nis possible to approximate almost  surely the partial sums of size $n$ of i.i.d. centered random \nvariables in ${\\mathbb L}^p$ ($p >2$) by a Wiener process with an \nerror term of order $o(n^{1\/p})$. In the case of functions of random iterates generated by an iid sequence, we\nwe shall give new dependent conditions, expressed in terms of a natural coupling (in ${\\mathbb L}^\\infty$ or in ${\\mathbb L}^1$), under which the strong approximation result holds with rate \n$o(n^{1\/p})$. The proof is an adaptation of the recent construction given in Berkes, Liu and Wu (2014).\nAs we shall see our conditions are well adapted to a  large variety of models, including left random\nwalks on $GL_d({\\mathbb R})$, contracting iterated random functions,  autoregressive Lipschitz processes,  and some ergodic Markov chains.\nWe shall also provide some examples showing that our ${\\mathbb L}^1$-coupling condition is in some sense optimal. This talk is based on a joint work with J. Dedecker and C. Cuny.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/68588?expand=metadata","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/extent":[{"value":"41.0","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/elements\/1.1\/format":[{"value":"video\/mp4","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":"","type":"literal","lang":"en"},{"value":"Author affiliation: University Paris Est Marne-la-Vall\u00e9e","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt":[{"value":"10.14288\/1.0376735","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/language":[{"value":"eng","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#peerReviewStatus":[{"value":"Unreviewed","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/provider":[{"value":"Vancouver : University of British Columbia Library","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/publisher":[{"value":"Banff International Research Station for Mathematical Innovation and Discovery","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/rights":[{"value":"Attribution-NonCommercial-NoDerivatives 4.0 International","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#rightsURI":[{"value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#scholarLevel":[{"value":"Faculty","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/isPartOf":[{"value":"BIRS Workshop Lecture Videos (Oaxaca de Ju\u00e1rez (Mexico))","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/subject":[{"value":"Mathematics","type":"literal","lang":"en"},{"value":"Probability theory and stochastic processes","type":"literal","lang":"en"},{"value":"Statistics","type":"literal","lang":"en"},{"value":"Probability \/ statistical mechanics","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/title":[{"value":"On strong approximations for some classes of random iterates","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/type":[{"value":"Moving Image","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#identifierURI":[{"value":"http:\/\/hdl.handle.net\/2429\/68588","type":"literal","lang":"en"}]}}