توضیحات
This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering. Read more…
Abstract: This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering
این کتاب یک رویکرد سیستماتیک و در دسترس برای معادلات دیفرانسیل تصادفی، معادلات دیفرانسیل تصادفی عقب مانده، و ارتباط آنها با معادلات دیفرانسیل جزئی، و همچنین توسعه اخیر نظریه کاملا غیرخطی، از جمله انتظارات غیرخطی، معادلات دیفرانسیل تصادفی عقب مانده مرتبه دوم، و معادلات دیفرانسیل جزئی وابسته به مسیر برنامههای اصلی و الگوریتمهای عددی و همچنین تمرینهای زیادی گنجانده شدهاند. این کتاب بر ایدهها و وضوح تمرکز دارد، اکثر نتایج از ابتدا حل شدهاند و بیشتر نظریهها از برنامههای کاربردی انگیزه دارند. این می تواند نقطه شروعی برای محققان جوان در این زمینه در نظر گرفته شود و می تواند به عنوان یک کتاب درسی برای یک دوره دو ترم تحصیلات تکمیلی در نظریه احتمالات و تحلیل تصادفی باشد. همچنین برای دانشجویان تحصیلات تکمیلی رشته مهندسی مالی قابل دسترسی است. ادامه مطلب…
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