Geodesic
One remark to the Itô formula
Teoriâ veroâtnostej i ee primeneniâ, Tome 69 (2024) no. 2, pp. 285-304 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the classical Itô formula, we propose replacing the second derivative (understood in the usual sense) by the second derivative in the sense of differentiation of distributions. In particular, we show that this can be done if the first derivative lies in the class $L_{2,\mathrm{loc}}(\mathbf{R})$. Earlier, Föllmer, Protter, and Shiryayev [Bernoulli, 1 (1995), pp. 149–169] obtained a different form of the last term in the Itô formula under the same conditions.
Keywords: random process, local time
Mots-clés : Itô formula, distribution. 
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I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. One remark to the Itô formula. Teoriâ veroâtnostej i ee primeneniâ, Tome 69 (2024) no. 2, pp. 285-304. http://geodesic.mathdoc.fr/item/TVP_2024_69_2_a5/

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