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Some results on probability theory can be generalized to more abstract ones in ergodic theory, for example: the strong law of large numbers can be seen as a particular case of Birkhoff's ergodic ...

I have a Markov Chain of $N$ states. Such states represent the energy levels in a molecule. The states' connectivity is as follows: States $j\in\{0,\ldots,N\}$ transition to $k\in\{\max(j-M,0),...,\...

Consider $w(t)$ as Guassian random process, with $w(t)$ being $\mathcal{N}(\mu,\sigma)$ and i.i.d for all t. I consider applying a (stochastic)derivative operation to the random process. What is the ...

I have several positive random variables $x_i,\ i=1,...,N$ taken from different unknown distributions (these distributions can be closely approximated by log-normal if needed). I can sample these ...

Motivation I am an economist writing a paper for an academic finance journal. My paper is about the behavior of currency traders, who choose the price at which they will sell currency today, based on ...

Hi, I am new to queueing theory. I am interested in a question that I feel should be fairly basic, yet I haven’t really found a clear solution to it. Hopefully somebody here can help me. We have a ...