Geodesic
On a family of random operators
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 3, pp. 544-564

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Random operators arising in the construction of probabilistic representation of the resolvent of the operator $-\frac{1}{2}\,\frac{d}{dx}\bigl(b^2(x)\frac{d}{dx}\bigr)$ are considered and shown to be integral with probability $1$. Properties of their kernels are investigated.
Keywords: random processes, local time, random operator. 
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     title = {On a family of random operators},
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I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. On a family of random operators. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 3, pp. 544-564. http://geodesic.mathdoc.fr/item/TVP_2023_68_3_a6/