Long-range dependence (LRD) refers to a phenomenon where a sequence of variables shows strong dependency. It has been observed in many areas such as earth science, internet traffic data, finance, etc. I am interested in modeling LRD and its application.
Self-similarity or fractal is observed widely in nature when similar shapes are repeated on an arbitrarily smaller scale. In the past, I have worked on estimating self-similarity, called fractal index, in stochastic processes and random fields. In the future, I am interested in modeling self-similarity in probability models.
Large deviation concerns the asymptotic behavior of rare events or small probabilities. I am interested in modeling dependency in rare events and estimating its asymptotic behavior.