Name: Singular Time-Homogeneous Ito Equations and PDEs (en Inglés)
SKU: 67494659
Price: 175.28 USD
Availability: InStock
Author: N. V. Krylov

portada Singular Time-Homogeneous Ito Equations and PDEs (en Inglés)

Singular Time-Homogeneous Ito Equations and PDEs (en Inglés)

Formato

Libro Físico

Editorial

American Mathematical Society

Autor

N. V. Krylov

Colección

Mathematical Surveys and Monographs

Año

2026

Idioma

Inglés

N° páginas

255

Encuadernación

Tapa Blanda

Dimensiones

25.4x17.8 cm

ISBN13

9781470485436

Singular Time-Homogeneous Ito Equations and PDEs (en Inglés)

N. V. Krylov (Autor) · American Mathematical Society · Tapa Blanda

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Reseña del libro "Singular Time-Homogeneous Ito Equations and PDEs (en Inglés)"

The aim of the book is to present some recent results in the theory of stochastic Ito equations with singular deterministic part (drift) and its applications to second-order elliptic and parabolic equations with singular first-order coefficients. The singularity is characterized by means of Morrey spaces, and this allows for much more singular coefficients than those from Lebesgue spaces. The first five chapters deal with equations having just measurable coefficients and treat the Markov diffusion processes $X$ corresponding to elliptic operators. In particular, Aleksandrov estimates, the Harnack inequality and the Holder continuity of $X$-harmonic functions are analyzed. This analysis requires the corresponding results in PDEs such as the extended Aleksandrov maximum principle, the Harnack inequality and the Holder continuity of PDE-harmonic functions. The three remaining chapters are devoted to the study of weak and strong solutions of Ito equations. This requires some regularity restrictions on the diffusion matrix (or second-order coefficients in the PDE language). The book provides the best to date conditions in terms of Morrey spaces for the existence and uniqueness of weak and strong solutions of Ito equations with singular drift. The majority of the results in the book are new even if the drift part is zero.