Geodesic
On nondegenerate Itô processes with moderated drift
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 3, pp. 630-660 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present an approach to proving parabolic Aleksandrov estimates with mixed norms for stochastic integrals with singular “moderated” drift.
Mots-clés : diffusion process, Itô process
Keywords: singular drift. 
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N. V. Krylov. On nondegenerate Itô processes with moderated drift. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 3, pp. 630-660. http://geodesic.mathdoc.fr/item/TVP_2023_68_3_a11/

[1] X. Cabré, “On the Alexandroff–Bakelman–Pucci estimate and the reversed Hölder inequality for solutions of elliptic and parabolic equations”, Comm. Pure Appl. Math., 48:5 (1995), 539–570 | DOI | MR | Zbl

[2] M. G. Crandall, M. Kocan, A. Świȩch, “$L^p$-theory for fully nonlinear uniformly parabolic equations”, Comm. Partial Differential Equations, 25:11-12 (2000), 1997–2053 | DOI | MR | Zbl

[3] Hongjie Dong, N. V. Krylov, “Aleksandrov's estimates for elliptic equations with drift in Morrey spaces containing $L_{d}$”, Proc. Amer. Math. Soc., 150:4 (2022), 1641–1645 | DOI | MR | Zbl

[4] E. B. Fabes, D. W. Stroock, “The $L^{p}$-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations”, Duke Math. J., 51:4 (1984), 997–1016 | DOI | MR | Zbl

[5] K. Fok, “A nonlinear Fabes–Stroock result”, Comm. Partial Differential Equations, 23:5-6 (1998), 967–983 | DOI | MR | Zbl

[6] M. Giaquinta, M. Struwe, “On the partial regularity of weak solutions of nonlinear parabolic systems”, Math. Z., 179:4 (1982), 437–451 | DOI | MR | Zbl

[7] N. V. Krylov, “Some estimates of the probability density of a stochastic integral”, Math. USSR-Izv., 8:1 (1974), 233–254 | DOI | MR | Zbl

[8] N. V. Krylov, Controlled diffusion processes, Appl. Math. (N. Y.), 14, Springer-Verlag, New York–Berlin, 1980, xii+308 pp. | DOI | MR | MR | Zbl | Zbl

[9] N. V. Krylov, “On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale”, Math. USSR-Sb., 58:1 (1987), 207–221 | DOI | MR | Zbl

[10] N. V. Krylov, “On time inhomogeneous stochastic Itô equations with drift in $L_{d+1}$”, Ukr. matem. zhurn., 72:9 (2020), 1232–1253 ; Ukrainian Math. J., 72:9 (2021), 1420–1444 | DOI | MR | Zbl | DOI

[11] N. V. Krylov, “On stochastic equations with drift in $L_d$”, Ann. Probab., 49:5 (2021), 2371–2398 | DOI | MR | Zbl

[12] N. V. Krylov, “On diffusion processes with drift in a Morrey class containing $L_{d+2}$”, J. Dynam. Differential Equations, 2021, 1–19, Publ. online | DOI

[13] N. V. Krylov, “Some properties of solutions of Itô equations with drift in $L_{d+1}$”, Stochastic Process. Appl., 147 (2022), 363–387 | DOI | MR | Zbl

[14] A. I. Nazarov, On the maximum principle for parabolic equations with unbounded coefficients, 2015, 14 pp., arXiv: 1507.05232 | MR

[15] A. I. Nazarov, N. N. Ural'tseva, “Convex-monotone hulls and an estimate of the maximum of the solution of a parabolic equation”, J. Soviet Math., 37 (1987), 851–859 | DOI | MR | Zbl