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Stochastic delay differential equations and related autoregressive models

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In this paper we suggest two continuous-time models which exhibit an autoregressive structure. We obtain existence and uniqueness results and study the structure of the solution processes. One of the models, which corresponds to general stochastic delay differential equations, will be given particular attention. We use the obtained results to link the introduced processes to both discrete-time and continuous-time ARMA processes.
Original languageEnglish
JournalStochastics: An International Journal of Probability and Stochastic Processes
Pages (from-to)454-477
Number of pages24
Publication statusPublished - 2020

    Research areas

  • Autoregressive structures, CARMA processes, long-range dependence, moving averages, processes of Ornstein-Uhlenbeck type, stochastic delay differential equations, 60G22, 60H10, 60G10, 60H20

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