Search results for "limit-theorems"

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A PHASE TRANSITION FOR LARGE VALUES OF BIFURCATING AUTOREGRESSIVE MODELS

2019

We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$ . The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive pr…

Statistics and Probability[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Phase transitionrandom environmentGeneral Mathematicsmedia_common.quotation_subjectmoderate deviationslimit-theoremsmarkov-chainsStatistics::Other StatisticsBranching processdeviation inequalities92D2501 natural sciencesAsymmetry010104 statistics & probability[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]Convergence (routing)[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]Applied mathematics60C05[MATH]Mathematics [math]0101 mathematicsautoregressive process60J20lawMathematicsBranching processmedia_commonEvent (probability theory)parametersconvergenceMarkov chain010102 general mathematics[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][MATH.MATH-PR]Mathematics [math]/Probability [math.PR]Large deviationslarge deviations Mathematics Subject Classification (2010): 60J8060K37Autoregressive modelcellsLarge deviations theoryStatistics Probability and Uncertaintyasymmetry60F10
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