Applied Stochastic Differential Equations
نویسنده
چکیده
Preface The purpose of these notes is to provide an introduction to to stochastic differential equations (SDEs) from applied point of view. Because the aim is in applications, much more emphasis is put into solution methods than to analysis of the theoretical properties of the equations. From pedagogical point of view the purpose of these notes is to provide an intuitive understanding in what SDEs are all about, and if the reader wishes to learn the formal theory later, he/she can read, for example, the brilliant books of Øksendal (2003) and Karatzas and Shreve (1991). The pedagogical aim is also to overcome one slight disadvantage in many SDE books (e.g., the above-mentioned ones), which is that they lean heavily on measure theory, rigorous probability theory, and to the theory martingales. There is nothing wrong in these theories—they are very powerful theories and everyone should indeed master them. However, when these theories are explicitly used in explaining SDEs, a lot of technical details need to be taken care of. When studying SDEs for the first time this tends to blur the basic ideas and intuition behind the theory. In this book, with no shame, we trade rigour to readability when treating SDEs completely without measure theory. In this book, we also aim to present a unified overview of numerical approximation methods for SDEs. Along with the Itô–Taylor series based simulation methods (Kloeden and Platen, 1999; Kloeden et al., 1994) we also present Gaussian approximation based methods which have and are still used a lot in the context of optimal
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تاریخ انتشار 2012