Random walks on the semi-axis. II. Limit distributions of boundary functionals

V. M. Šurenkov

Kiev

Abstract: We prove some limit theorems for the joint distributions of values $\tau_z,x_{\tau_z},i_{\tau_z}(z\to\infty)$, where $\tau_z=\inf\{t\colon x_t\ge z\}$ and $(i_t,x_t)$, $t\ge 0$, is the homogeneous Markov–Feller process in the phase space $\{1,\dots,d\}\times[0,\infty)$ which is additive in the second component and has no negative jumps.

Received: 15.06.1978

 English version: Theory of Probability and its Applications, 1982, 26:3, 452–467

Bibliographic databases:

• 
• 
•