Geodesic
On a family of complex-valued stochastic processes
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 38-41

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We introduce a family $r_\lambda$, $\lambda\in\mathbb C$ of complex-valued stochastic processes making it possible to construct a probabilistic representation for the resolvent of the operator $-\frac12\frac{d^2}{dx^2}$. For $\lambda=0$ the process $r_\lambda$ is real-valued and coincides with the Brownian local time process.
Keywords: random processes, local time. 
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     author = {I. A. Ibragimov and N. V. Smorodina and M. M. Faddeev},
     title = {On a family of complex-valued stochastic processes},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {38--41},
     publisher = {mathdoc},
     volume = {501},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_501_a6/}
}
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I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. On a family of complex-valued stochastic processes. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 38-41. http://geodesic.mathdoc.fr/item/DANMA_2021_501_a6/