On the dependence structure of certain multi-dimensional Ito processes and corresponding hitting times. (English) Zbl 1175.90120
From the abstract: Let \(X(t)=(X_1(t),X_2(t),\dots, X_k(t))\), \(t\geq 0\) be an Itô process assuming values in \(\mathbb{R}^k\). We show that, under certain conditions, the process \(X(t)\) has a certain dependence structure. We also consider the first passage problem involving \(X(t)\) and discuss the dependence structure among hitting times of \(X_1(t),\dots,X_k(t)\).
MSC:
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
| 60K10 | Applications of renewal theory (reliability, demand theory, etc.) |
| 62N05 | Reliability and life testing |
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