From the reviews: JOURNAL OF THE AMERICAN STOCHASTIC ASSOCIATION "The material is accessible to researchers and advanced graduate students. These two classic volumes are very important resources for both probabilists and statisticians." SIAM REVIEW "Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering...What is special about these books is their broad coverage and in-depth study of optimal filtering problems...The books can be used by researchers in different areas who need to use stochastic calculus and who treat state estimation, detection, and stochastic control problems under incomplete information and partial observations...These two books are a comprehensive treatise on stochastic calculus, random processes, and filtering theory, and provide an excellent and illuminating introduction to these fields with a wide range of theoretical and practical issues. With the new additions and modifications of the first edition, they are to be welcomed and benefit not only the systems theory and control community but also mathematicians working on stochastic processes; engineers in control, communication, and signal processing; researchers in financial engineering; and scientists in many other related fields. It is conceivable that these books will have a significant impact on the aforementioned fields and will become classics." SIAM REVIEW "...and the second volume can be used as a text for a special topics course in filtering."