Higher order asymptotic expansions for weakly correlated random functions [Elektronische Ressource] / vorgelegt von Hans-Jörg Starkloff

Higher order asymptoticexpansions for weakly correlatedrandom functionsVon der Fakult¨at fu¨r Mathematikder Technischen Universit¨at ChemnitzgenehmigteHabilitationsschriftzur Erlangung des akademischen Gradesdoctor rerum naturalium habilitatus(Dr. rer. nat. habil.)vorgelegt vonHans-J¨org StarkloffChemnitz, Januar 20051PrefaceIn mathematical modelling often uncertainties occur, which in a number of caseshave tobe taken into consideration formore realistic calculations. If these uncer-tainties obey some statistical regularity they can be described as random quan-tities. This leads to the task to investigate random equations, especially randomdifferential equations. Due to general difficulties which arise solving randomequations often approximations and simplifying assumptions are made.Approximate characteristics of solutions to random differential equations can befound, if the occuring random parameter functions belong to a class of weaklydependent random functions orcan be represented as integral functionals ofsuchfunctions. Here two points play a central role.1. In exact or approximate solution procedures often integral functionals ofparameter functions of the differential equation occur.2. For such integral functionals with weakly dependent parameter functionsstatistical characteristics like moments canbe calculated approximately us-ing an asymptotic analysis.