Geodesic
Distributions of It\^o processes: estimates for the density and for conditional expectations of integral functionals
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 4, pp. 825-833

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We obtain a priori estimates for the $L_2$-norms of solutions of parabolic Itô equations describing evolution of the distributions of solutions of ordinary Itô stochastic differential equations with random coefficients. In the case of nondegenerate equations, estimates for the $L_2$-norms of derivatives with respect to space variables are also obtained. As a consequence, we establish a generalisation of Itô's formula for functions that have only square-summable derivatives of the first and the second order (or even of the first order).
Keywords: distributions of Itô, processes
Mots-clés : parabolic Itô, equations, Itô's formula. 
@article{TVP_1994_39_4_a13,
     author = {N. G. Dokuchaev},
     title = {Distributions of {It\^o} processes: estimates for the density and for conditional expectations of integral functionals},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {825--833},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a13/}
}
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N. G. Dokuchaev. Distributions of It\^o processes: estimates for the density and for conditional expectations of integral functionals. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 4, pp. 825-833. http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a13/