{"title":"Hiroshi Kunita","description":null,"products":[{"product_id":"stochastic-flows-and-stochastic-differential-equations-book-hiroshi-kunita-9780521599252","title":"Stochastic Flows and Stochastic Differential Equations","description":"Stochastic analysis and stochastic differential equations are rapidly developing fields in probability theory and its applications. This book provides a systematic treatment of stochastic differential equations and stochastic flow of diffeomorphisms and describes the properties of stochastic flows. Professor Kunita's approach regards the stochastic differential equation as a dynamical system driven by a random vector field, including K. It 's classical theory. Beginning with a discussion of Markov processes, martingales and Brownian motion, Kunita reviews It 's stochastic analysis. He places emphasis on establishing that the solution defines a flow of diffeomorphisms. This flow property is basic in the modern and comprehensive analysis of the solution and will be applied to solve the first and second order stochastic partial differential equations. This book will be valued by graduate students and researchers in probability. It can also be used as a textbook for advanced probability courses.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52403045662993,"sku":"NLS9780521599252","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52735440191761,"sku":"NIN9780521599252","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521599252.jpg?v=1758759665"},{"product_id":"stochastic-flows-and-jump-diffusions-book-hiroshi-kunita-9789811338007","title":"Stochastic Flows and Jump-Diffusions","description":"This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps.In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heatequations are constructed independently of the theory of partial differential equations.Researchers and graduate student in probability theory will find this book very useful.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52478954963217,"sku":"NLS9789811338007","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53015577493777,"sku":"NIN9789811338007","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789811338007.jpg?v=1759847952"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-hiroshi-kunita.oembed","provider":"World of Books ","version":"1.0","type":"link"}