聖塔非研究所

摘要 Virtually all questions that one can ask about th

2018-03-01 · 已發表論文 · 更新 2026/08/30 下午12:48

摘要 Virtually all questions that one can ask about the behavioral and structural complexity of a 隨機 process reduce to a linear algebraic framing of a time 演化 governed by an appropriate hidden…

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  • 類型:已發表論文
  • 日期:2018-03-01

摘要

Virtually all questions that one can ask about the behavioral and structural complexity of a 隨機 process reduce to a linear algebraic framing of a time 演化 governed by an appropriate hidden-馬可夫 process generator. Each type of question-correlation, predictability, predictive cost, observer 同步化, and the like-induces a distinct generator class. Answers are then functions of the class-appropriate transition dynamic. Unfortunately, these dynamics are generically nonnormal, nondiagonalizable, singular, and so on. Tractably analyzing these dynamics relies on adapting the recently introduced meromorphic functional calculus, which specifies the spectral decomposition of functions of nondiagonalizable linear operators, even when the function poles and zeros coincide with the operator's spectrum. Along

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