4 problems

Let $J^{\rm c}$ be the competitive window and consider the Stigler–Luckock model restricted to $J^{\rm c}$. A Markov process is null recurrent when it returns recurrently but has n…

Let $X_k$ be the Stigler–Luckock order-book process, let $J^{\rm c}$ be its competitive window, and let $X_k\big|_{J^{\rm c}}$ denote the restriction of the order book to that wind…

Let $(X_k)_{k\geq 0}$ be the discrete-time Stigler–Luckock order-book process, let $M_-(X_k)$ and $M_+(X_k)$ denote its best buy and sell orders, and let $\lambda_-$ and…

Let $(f_-,f_+)$ be the solution to Luckock's equation for a Stigler–Luckock model, and call it valid when $f_-(I_-)\wedge f_+(I_+)\geq 0$. An invariant law is a probability law pre…