This book is a systematic, rigorous, and self-consistent introduction to the theory of continuous-time stochastic processes. But it is neither a tract nor a recipe book as such; rather, it is an account of fundamental concepts as they appear in relevant modern applications and literature. We make no pretense of it being complete. Indeed, we have omitted many results, which we feel are not directly related to the main theme or that are available in easily accessible sources. (Those readers who are interested in the historical development of the subject cannot ignore the volume edited by Wax (1954).)
Proofs are often omitted as technicalities might distract the reader from a conceptual approach. They are produced whenever they may serve as a guide to the introduction of new concepts and methods towards the appli- cations; otherwise, explicit references to standard literature are provided. A mathematically oriented student may find it interesting to consider proofs as exercises.
The scope of the book is profoundly educational, related to modeling real- world problems with stochastic methods. The reader becomes critically aware of the concepts involved in current applied literature, and is moreover provided with a firm foundation of the mathematical techniques. Intuition is always supported by mathematical rigor.