In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class (A) F = F is continuous and concave; F (t) ≤ t for t ≥ 0.. Note that all possible asymptotics are absolutely continuous.

The paper considers a particular family of set–valued continuous time stochastic processes modeling birth–and–growth processes. The proposed setting allows us to infer the nucleation and the growth processes. A decomposition theorem is established to characterize the nucleation and the growth. As a logical consequence, different consistent set–valued estimators are studied for growth process. M...

This paper studies a two-player zero-sum Dynkin game arising from pricing an option on asset whose rate of return is unknown to both players. Using filtering techniques, we first reduce the problem bidimensional diffusion (X,Y). Then characterize existence Nash equilibrium in pure strategies which each player stops at hitting time (X,Y) set with moving boundary. A detailed description stopping ...

Let $T_{\rho}$ be an irrational rotation on a unit circle $S^{1}\simeq [0,1)$. Consider the sequence $\{\mathcal{P}_{n}\}$ of increasing partitions $S^{1}$. Define hitting times $N_{n}(\mathcal{P}_n;x,y):= \inf\{j\geq 1\mid T^{j}_{\rho}(y)\in P_{n}(x)\}$, where $P_{n}(x)$ is element $\mathcal{P}_{n}$ containing $x$. D. Kim and B. Seo in [9] proved that rescaled $K_n(\mathcal{Q}_n;x,y):= \frac{\...