TY - JOUR
T1 - A new proof of an Engelbert-Schmidt type zero-one law for time-homogeneous diffusions
AU - Cui, Zhenyu
PY - 2014/6
Y1 - 2014/6
N2 - In this paper we give a new proof to an Engelbert-Schmidt type zero-one law for time-homogeneous diffusions, which provides deterministic criteria for the convergence of integral functional of diffusions. Our proof is based on a slightly stronger assumption than that in Mijatović and Urusov (2012a) and utilizes stochastic time change and Feller's test of explosions. It does not rely on advanced methods such as the first Ray-Knight theorem, William's theorem, Shepp's dichotomy result for Gaussian processes or Jeulin's lemma as in the previous literature (see Mijatović and Urusov (2012a) for a pointer to the literature). The new proof has an intuitive interpretation as we link the integral functional to the explosion time of an associated diffusion process.
AB - In this paper we give a new proof to an Engelbert-Schmidt type zero-one law for time-homogeneous diffusions, which provides deterministic criteria for the convergence of integral functional of diffusions. Our proof is based on a slightly stronger assumption than that in Mijatović and Urusov (2012a) and utilizes stochastic time change and Feller's test of explosions. It does not rely on advanced methods such as the first Ray-Knight theorem, William's theorem, Shepp's dichotomy result for Gaussian processes or Jeulin's lemma as in the previous literature (see Mijatović and Urusov (2012a) for a pointer to the literature). The new proof has an intuitive interpretation as we link the integral functional to the explosion time of an associated diffusion process.
KW - Diffusion
KW - Engelbert-Schmidt type zero-one law
KW - Integral functional
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U2 - 10.1016/j.spl.2014.03.003
DO - 10.1016/j.spl.2014.03.003
M3 - Article
AN - SCOPUS:84897843089
SN - 0167-7152
VL - 89
SP - 118
EP - 123
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
IS - 1
ER -