{"product_id":"analytic-theory-of-ito-stochastic-differential-equations-with-non-smooth-coefficients-von-haesung-lee-wilhelm-stannat-und-gerald-trutnau","title":"Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients","description":"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 \u003ci\u003eL\u003c\/i\u003e\n                \u003csup\u003e\n                    \u003ci\u003ep\u003c\/i\u003e\n                \u003c\/sup\u003e-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.\u003cbr\u003e\n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789811938306\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9789811938306","offer_id":40477391650909,"sku":"9789811938306","price":58.84,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/62477121-aeb2-4d17-a562-784cebf927ac.jpg?v=1772175082","url":"https:\/\/shop.autorenwelt.de\/products\/analytic-theory-of-ito-stochastic-differential-equations-with-non-smooth-coefficients-von-haesung-lee-wilhelm-stannat-und-gerald-trutnau","provider":"Autorenwelt Shop","version":"1.0","type":"link"}