The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
\(
\newcommand{\P}[]{\unicode{xB6}}
\newcommand{\AA}[]{\unicode{x212B}}
\newcommand{\empty}[]{\emptyset}
\newcommand{\O}[]{\emptyset}
\newcommand{\Alpha}[]{Α}
\newcommand{\Beta}[]{Β}
\newcommand{\Epsilon}[]{Ε}
\newcommand{\Iota}[]{Ι}
\newcommand{\Kappa}[]{Κ}
\newcommand{\Rho}[]{Ρ}
\newcommand{\Tau}[]{Τ}
\newcommand{\Zeta}[]{Ζ}
\newcommand{\Mu}[]{\unicode{x039C}}
\newcommand{\Chi}[]{Χ}
\newcommand{\Eta}[]{\unicode{x0397}}
\newcommand{\Nu}[]{\unicode{x039D}}
\newcommand{\Omicron}[]{\unicode{x039F}}
\DeclareMathOperator{\sgn}{sgn}
\def\oiint{\mathop{\vcenter{\mathchoice{\huge\unicode{x222F}\,}{\unicode{x222F}}{\unicode{x222F}}{\unicode{x222F}}}\,}\nolimits}
\def\oiiint{\mathop{\vcenter{\mathchoice{\huge\unicode{x2230}\,}{\unicode{x2230}}{\unicode{x2230}}{\unicode{x2230}}}\,}\nolimits}
\)
Stochastic Process as taught in Durett's Book in STAT650.
Markov Chains
Poisson Processes
The following 3 definitions of the Poisson process are equivalent.
- A Poisson process with rate \(\displaystyle \lambda\) is a counting process where the number of arrivals \(\displaystyle N(s+t)-N(s)\) in a given time period \(\displaystyle t\) has distribution \(\displaystyle Poisson(\lambda t)\)
- A Poisson process is a renewal process with rate \(\displaystyle 1/\lambda\)
- A Poisson process is a continuous time markov chain with \(\displaystyle P(N(h)=1) = \lambda h + o(h)\) and \(\displaystyle P(N(h) \geq 2) = o(h)\)
Renewal Processes
Queueing Theory
