Name: Analytic Theory of Itô-Stochastic Differential Equations with Non-Smooth Coefficients (en Inglés)
SKU: 59446791
Price: 1004.07 MXN
Availability: InStock
Author: Lee, Haesung ; Stannat, Wilhelm ; Trutnau, Gerald
ISBN: 9789811938306

portada Analytic Theory of Itô-Stochastic Differential Equations with Non-Smooth Coefficients (en Inglés)

Analytic Theory of Itô-Stochastic Differential Equations with Non-Smooth Coefficients (en Inglés)

Formato

Libro Físico

Autor

Editorial

Idioma

Inglés

N° páginas

126

Encuadernación

Tapa Blanda

Dimensiones

23.4x15.6x0.8 cm

Peso

0.21 kg.

ISBN13

9789811938306

Categorías

Cálculo diferencial y ecuaciones
Probabilidad y estadística

Analytic Theory of Itô-Stochastic Differential Equations with Non-Smooth Coefficients (en Inglés)

Haesung Lee (Autor) · Wilhelm Stannat (Autor) · Gerald Trutnau (Autor) · Springer · Tapa Blanda

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Reseña del libro "Analytic Theory of Itô-Stochastic Differential Equations with Non-Smooth Coefficients (en Inglés)"

This book provides analytic tools to describe local and global behavior of solutions to Itô-stochastic differential equations with non-degenerate Sobolev diffusion coefficients and locally integrable drift. Regularity theory of partial differential equations is applied to construct such solutions and to obtain strong Feller properties, irreducibility, Krylov-type estimates, moment inequalities, various types of non-explosion criteria, and long time behavior, e.g., transience, recurrence, and convergence to stationarity. The approach is based on the realization of the transition semigroup associated with the solution of a stochastic differential equation as a strongly continuous semigroup in the Lp-space with respect to a weight that plays the role of a sub-stationary or stationary density. This way we obtain in particular a rigorous functional analytic description of the generator of the solution of a stochastic differential equation and its full domain. The existence of such a weight is shown under broad assumptions on the coefficients. A remarkable fact is that although the weight may not be unique, many important results are independent of it. Given such a weight and semigroup, one can construct and further analyze in detail a weak solution to the stochastic differential equation combining variational techniques, regularity theory for partial differential equations, potential, and generalized Dirichlet form theory. Under classical-like or various other criteria for non-explosion we obtain as one of our main applications the existence of a pathwise unique and strong solution with an infinite lifetime. These results substantially supplement the classical case of locally Lipschitz or monotone coefficients.We further treat other types of uniqueness and non-uniqueness questions, such as uniqueness and non-uniqueness of the mentioned weights and uniqueness in law, in a certain sense, of the solution.