Statistical inference in actuarial, engineering, and life sciences

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There are numerous unresolved problems in actuarial, engineering, life and other sciences dealing with sequences, functions, and their functionals. The proposed research program has two intertwined objectives: A) creating and exploring appropriate statistical models and improving upon existing ones, and B) producing appropriate statistical inferential theories and testing them in simulation studies as well as on real data. Specific problems of my particular interest concern such areas as: 1) modeling ageing processes in biological, electrical, and mechanical systems with applications in actuarial, life, and engineering sciences, 2) statistical reliability engineering with the aim at determining and investigating optimal burn-in, wear-out, replacement policies, 3) developing tests for distinguishing deterministic noises from random ones with applications in medical sciences and telecommunications. These research areas give rise to most interesting statistical and probabilistic problems as well as to challenges in applied and pure mathematics.