Summary
Let (X(t), t∈S) be a real-valued stochastic process with ℙ(X(0)=0)=1 and\(\mathbb{P} (\mathop {\lim }\limits_{t \to \infty } X(t) = \infty ) = 1\). In this paper we are interested in the reluctance of such a process to tend to infinity. This entails determining the rate of escape of the associated process\((\mathop {\inf }\limits_{s\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \geqslant } t} X(s), t \in S)\), the so-calledfuture infima process.
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Research supported by NSF grant DMS-9122242
Research supported by NSF grants DMS-9122242 and DMS-9024961
Research supported by NSF grants DMS-9024961 and DMS-8901545
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Khoshnevisan, D., Lewis, T.M. & Li, W.V. On the future infima of some transient processes. Probab. Th. Rel. Fields 99, 337–360 (1994). https://doi.org/10.1007/BF01199896
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DOI: https://doi.org/10.1007/BF01199896