The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock ...

Let (S¯1, S¯2) be the two-sided random walks in ℤ𝑑 (𝑑 = 2, 3) conditioned so that S¯1[0,∞)∩S¯2[1,∞)=∅, which was constructed by the author in 2012. We prove that the number of global cut times up to ...

The steps of a one-dimensional random walk are positive and occur randomly in time at a fixed mean rate. The sizes of the steps are independent and the size of each step has the same given probability ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...