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1. Definitions Definition 1. We say the process \(\{X(t),t\ge0\}\) is a continuous-time Markov chain if for all \(s,t\ge0\) and nonnegative integers 阅读全文
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1. Introduction Let \(\{X_n,n=0,1,2,...\}\) be a stochastic process that takes on a finite number of possible values. If \(X_n=i\), then the process 阅读全文
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1. Basic properties and examples 1.1 Definitions A function \(f:\R^n\rarr\R\) is convex if \(\mathrm{\textbf{dom}}\ f\) is a convex set and if for a 阅读全文
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1. Counting process We say that \(\{N(t),t\ge0\}\) is a counting process if \(N(t)\) represents the total number of "events" occur by time \(t\) and 阅读全文