Zobrazeno 1 - 10
of 170
pro vyhledávání: '"Nicolai V Krylov"'
Autor:
Nicolai V Krylov
Publikováno v:
Stochastic Processes and their Applications. 138:1-25
For Ito stochastic processes in R d with drift in L d Aleksandrov’s type estimates are established in the elliptic and parabolic settings. They are applied to estimating the resolvent operators of the corresponding elliptic and parabolic operators
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6741979df04f08aeb63855e5d1f420cf
https://doi.org/10.1016/j.spa.2021.04.005
https://doi.org/10.1016/j.spa.2021.04.005
Autor:
Nicolai V Krylov
Publikováno v:
St. Petersburg Mathematical Journal. 32:389-413
This is a brief historical overview of the Sobolev mixed norm theory of linear elliptic and parabolic equations and the recent development in this theory based on the Rubio de Francia extrapolation theorem. A self-contained proof of this theorem alon
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::50d459f14205995db50c554b765b8002
https://doi.org/10.1090/spmj/1653
https://doi.org/10.1090/spmj/1653
Autor:
Nicolai V Krylov
Publikováno v:
Ukrainian Mathematical Journal. 72:1420-1444
We prove the solvability of Ito stochastic equations with uniformly nondegenerate bounded measurable diffusion and drift in Ld+1(Rd+1). Actually, the powers of summability of the drift in x and t could be different. Our results seem to be new even if
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::02c517b52c24b7b355654464d245eb63
https://doi.org/10.1007/s11253-021-01864-8
https://doi.org/10.1007/s11253-021-01864-8
Autor:
Nicolai V Krylov
Publikováno v:
Transactions of the American Mathematical Society. 374:2805-2822
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d9c54f52a91e7315a35f29a9a9ff92e1
https://doi.org/10.1090/tran/8282
https://doi.org/10.1090/tran/8282
Autor:
Nicolai V Krylov
Publikováno v:
Probability Theory and Related Fields. 179:165-199
We investigate properties of Markov quasi-diffusion processes corresponding to elliptic operators $$L=a^{ij}D_{ij}+b^{i}D_{i}$$ , acting on functions on $$\mathbb {R}^{d}$$ , with measurable coefficients, bounded and uniformly elliptic a and $$b\in L
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f4b8943e3a5dd13f73b9b591bcdae294
https://doi.org/10.1007/s00440-020-01007-3
https://doi.org/10.1007/s00440-020-01007-3
Autor:
Nicolai V Krylov
Publikováno v:
Communications in Partial Differential Equations. 45:1778-1798
In subdomains of R d , we consider uniformly elliptic equations H ( v ( x ) , D v ( x ) , D 2 v ( x ) , x ) = 0 with the growth of H with respect to | D v | controlled by the product of a function ...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ceef188d9f6263aaf907101851d5a774
https://doi.org/10.1080/03605302.2020.1805462
https://doi.org/10.1080/03605302.2020.1805462
Autor:
Nicolai V Krylov
Publikováno v:
St. Petersburg Mathematical Journal. 31:509-520
We prove several pointwise estimates for solutions of linear elliptic (parabolic) equations with measurable coefficients in smooth domains (cylinders) through the weighted $L_{d}$ ($L_{d+1}$)-norm of the free term. The weights allow the free term to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a78f3018a69dbc0d8051f36da88b5d4e
https://doi.org/10.1090/spmj/1611
https://doi.org/10.1090/spmj/1611
Autor:
Nicolai V Krylov
Publikováno v:
Stochastic Processes and their Applications. 130:1426-1434
We give error estimates in Peng’s central limit theorem for not necessarily nondegenerate case. The exposition uses the language of the classical probability theory instead of the language of the theory of sublinear expectations. We only consider t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a9bdf2e2d89fc7cd23947c331499932e
https://doi.org/10.1016/j.spa.2019.05.005
https://doi.org/10.1016/j.spa.2019.05.005
Autor:
Nicolai V Krylov
Publikováno v:
Journal of Dynamics and Differential Equations.
We present new conditions on the drift of the Morrey type with mixed norms allowing us to obtain Aleksandrov type estimates of potentials of time inhomogeneous diffusion processes in spaces with mixed norms and, for instance, in $$L_{d_{0}+1}$$ with
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f7bcd2f1ea57a16a896dc12c5d7acbf2
https://doi.org/10.1007/s10884-021-10099-x
https://doi.org/10.1007/s10884-021-10099-x
Autor:
Hongjie Dong, Nicolai V. Krylov
Publikováno v:
Electronic Journal of Differential Equations, Vol 2005, Iss 102, Pp 1-25 (2005)
We consider degenerate parabolic and elliptic equations of second order with $C^1$ and $C^2$ coefficients. Error bounds for certain types of finite-difference schemes are obtained.
Externí odkaz:
https://doaj.org/article/105facce02274417b901c14866eb5b64