Gawarecki, Leszek.
Stochastic Differential Equations in Infinite Dimensions with Applications to Stochastic Partial Differential Equations / [electronic resource] : by Leszek Gawarecki, Vidyadhar Mandrekar. - XVI, 292 p. online resource. - Probability and Its Applications, 1431-7028 . - Probability and Its Applications, .
Preface -- Part I: Stochastic Differential Equations in Infinite Dimensions -- 1.Partial Differential Equations as Equations in Infinite -- 2.Stochastic Calculus -- 3.Stochastic Differential Equations -- 4.Solutions by Variational Method -- 5.Stochastic Differential Equations with Discontinuous Drift -- Part II: Stability, Boundedness, and Invariant Measures -- 6.Stability Theory for Strong and Mild Solutions -- 7.Ultimate Boundedness and Invariant Measure -- References -- Index.
The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.
9783642161940
10.1007/978-3-642-16194-0 doi
Mathematics.
Differential equations, partial.
Finance.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Partial Differential Equations.
Quantitative Finance.
Applications of Mathematics.
QA273.A1-274.9 QA274-274.9
519.2
Stochastic Differential Equations in Infinite Dimensions with Applications to Stochastic Partial Differential Equations / [electronic resource] : by Leszek Gawarecki, Vidyadhar Mandrekar. - XVI, 292 p. online resource. - Probability and Its Applications, 1431-7028 . - Probability and Its Applications, .
Preface -- Part I: Stochastic Differential Equations in Infinite Dimensions -- 1.Partial Differential Equations as Equations in Infinite -- 2.Stochastic Calculus -- 3.Stochastic Differential Equations -- 4.Solutions by Variational Method -- 5.Stochastic Differential Equations with Discontinuous Drift -- Part II: Stability, Boundedness, and Invariant Measures -- 6.Stability Theory for Strong and Mild Solutions -- 7.Ultimate Boundedness and Invariant Measure -- References -- Index.
The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.
9783642161940
10.1007/978-3-642-16194-0 doi
Mathematics.
Differential equations, partial.
Finance.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Partial Differential Equations.
Quantitative Finance.
Applications of Mathematics.
QA273.A1-274.9 QA274-274.9
519.2