11 problems

Consider a countably infinite state space with $lambda_i>0$ for all $i\geq 0$, $mu_i>0$ for all $i\geq 1$, retention probabilities $q_i^\pm$ defined for all $i\geq 0$ with…

Let $S$ be a denumerably infinite state space, and let $\{X_n\}_{n=0}^\infty$ be a positive recurrent, discrete-time Markov chain on $S$ with invariant probability measure $\mu$. F…

Equality conjecture. Then

Normalized SRLP conjecture. We have

Countable-label extension conjecture. We conjecture that the results of the paper continue to hold for this countable-label model.

Let $H$ be the nonlinearity identified as the limit of the scaled flow … where $\phi_t$ is generated by the differential equation in the fluid approximation. Higher-dimensional per…

Let $p\geq 3$, and let $\lambda_n$ and $\mu_n$ be birth and death rates that are polynomials of degree $p$ with … … Assume that $1<C-D<p-1$. Valent's conjecture. The order of the c…

Valent's conjecture. For this indeterminate Stieltjes moment problem, the order, type, and Phragmén–Lindelöf indicator function are

Roehner–Valent conjecture. The operator has no eigenvalues:

Let ${\bar\delta}_n$ and $\delta_n'$ be the quantities defined in Theorem 4.3. Stability-bound conjecture. One has … The conjecture is supported by all examples computed in the sou…

Recurrence threshold conjecture. If $\lambda=U_s$, the process is positive recurrent if $0 < \mu < \mu_o$ and is null recurrent if $\mu > \mu_o$.