9 problems

Polynomial property conjecture. There exists such a process $Y$ for which $q(t,\cdot)\in\mathcal{P}_m$ for every $m\in\mathbb{N}$, every $u\in\mathcal{P}_m$, and every $t\geq 0$.

Semi-Markov property conjecture. The process $X$ is semi-Markov, even in the general case in which $E$ is a locally compact separable Hausdorff space.

Let $S$ be the state space of the semi-Markov process, and let Proposition 4.4 denote the proposition asserting the stated characterization involving the variances $\sigma_j^2$ and…

Let $I_{t}^{(a,b)}$ denote the stochastic integral process studied in the paper, and suppose the model is in one of the divergent cases. Let $a'(\cdot)$ and $b'(\cdot)$ be suitable…

Let $S$ be a finite state space, let Assumption 0 hold, and consider the quantity … Suppose this quantity is regularly varying with index $\alpha\in(1,2)$. Reverse regular-variatio…

Computational tractability conjecture. The baseline semi-Markov approximation setup can be extended to this valuation problem in order to achieve computational tractability. This w…

The paper considers option prices written on a continuous-time multiplicative semi-Markov process and, under suitable scaling, their convergence to the option price for an underlyi…

Reduction conjecture. The model can be reduced to the corresponding model for regularly and singularly perturbed two-state semi-Markov processes by aggregating regenerative periods…

Let $X_n^c$ and $T_n^c$ be scaled coupled processes converging weakly, as $c\to 0$, to a process $(A(t),D(t))$, and let $E(t)$ be the hitting time of $D$. In the heterogeneous sett…