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XXXIV International Seminar on Stability Problems for Stochastic Models will be held between 25-29 August, 2017 in Debrecen, Hungary under the auspices of Faculty of Informatics, University of Debrecen, Lomonosov Moscow State University and Institute of Informatics Problems of the Russian Academy of Sciences. The Seminar is sponsored by the Bernoulli Society. Seminars on Stability Problems for Stochastic Models have a long tradition. They were founded by Vladimir Zolotarev in the 1970’s. The seminars were attended by leading probabilists from all over the world and traditionally aim at bringing together people from Eastern and Western parts of Europe to share their expertise, new results, exchange the ideas and discuss open problems. Previous three Seminars took place in Svetlogorsk Russia (2016), in Trondheim, Norway (2014) and in Moscow Russia (2013).