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Analytic Theory of Ito-Stochastic Differential Equations with Non-smooth Coefficients
Af: Gerald Trutnau, Haesung Lee, Wilhelm Stannat
Engelsk
Bogcover for Analytic Theory of Ito-Stochastic Differential Equations with Non-smooth Coefficients af Gerald Trutnau, Haesung Lee, Wilhelm Stannat, 9789811938306
Specifikationer
Sprog:
Engelsk
Sider:
126
ISBN-13:
9789811938306
Indbinding:
Paperback
ISBN-10:
981193830X
Kategori:
Udg. Dato:
28 aug 2022
Størrelse i cm:
23,5 x 15,5
Forlag:
Serie:
Oplagsdato:
28 aug 2022
Forfatter(e):
Genre:

Analytic Theory of Ito-Stochastic Differential Equations with Non-smooth Coefficients

Af: Gerald Trutnau, Haesung Lee, Wilhelm Stannat
Engelsk
Paperback 2022
Format:
Paperback
Bog beskrivelse
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.

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Specifikationer
Sprog:
Engelsk
Sider:
126
ISBN-13:
9789811938306
Indbinding:
Paperback
ISBN-10:
981193830X
Kategori:
Udg. Dato:
28 aug 2022
Størrelse i cm:
23,5 x 15,5
Forlag:
Serie:
Oplagsdato:
28 aug 2022
Forfatter(e):
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