331 pp. and 337 pp., $21.60 each M. Iosifescu, P. Tǎutu, ,Stochastic Processes and Applications in Biology and Medicine. Part 1—Theory. Part 2—Models (1973) Springer-Verlag.
✍ Scribed by Per-Erik E. Bergner
- Publisher
- Springer
- Year
- 1974
- Tongue
- English
- Weight
- 294 KB
- Volume
- 36
- Category
- Article
- ISSN
- 1522-9602
No coin nor oath required. For personal study only.
✦ Synopsis
There seem to be three main reasons (not mutually exclusive) for applying the theory of stochastic processes:
(i) one can derive parameters t h a t are meaningful when d a t a exhibit r a n d o m variation; (ii) one can deduce macroscopic random behavior from hypotheses concerning the underlying microscopic (e.g. physical) mechanisms; (iii) one can discuss in a formal and precise way different and physically complex processes, and recognize their similarities, without invoking any specific (physical) models. As obvious examples of (i) we h a v e parameters such as m e a n and variance; a somewhat more sophisticated example is the death rate as a function of age. E x a m p l e s of (ii) are the study of scattering of high-energy particles and various forms of diffusion.
W e have to be somewhat careful when it comes to (iii). F o r instance, it occasionally happens that, say, chemical rate constants are referred to as transition probabilities but t h a t alone does not m a k e the analysis stochastic; whether or not an approach is stochastic can hardly be a mere question of terminology. Hence, for an analysis to be stochastic, we should require something more, for instance t h a t certain experimentally accessible relations are derived on the basis of probability theory. A nice example is the similarity between some equations in reliability theory of system engineering and the equations in some forms of cell kinetics; in b o t h instances, the equations reside on elementary probabilistie arguments.
During the 'fifties and 'sixties there was some scepticism regarding the future of the theory of stochastic processes. The reason was that the theory of stochastic processes leads to depressingly complicated m a t h e m a t i c a l expressions already when applied to physically oversimplified models. I-Iowever, the recent c o m p u t e r generations have changed the situation: Monte Carlo simulations that some years ago were a possibility for only a few selected, are t o d a y at the finger-tips of a substantial n u m b e r of scientists--and this number is increasing. As a consequence, there seems to be an increasing interest in the basic mathematical structure of the theory. P a r t 1 exemplifies this trend: the text is entirely devoted to m a t h e m a t i c a l aspects of the theory of stochastic processes. The reader is exposed to a rather comprehensive text that, however, also contains sources of frustration. Thus, the authors' only m o t i v a t i o n for their writing is seemingly formalistie: t h e y tell us, over and over again, that a very import a n t consequence of some equation i s . . . and then follows the new equation, and t h a t is it; this new equation is never mentioned again, and its importance remains a question. Phrased differently, one receives the impression t h a t the only connection between subsections is that t h e y are printed together. This is a catalogue! Thus, in spite of certain elegance of isolated paragraphs, after about 40 pages, I was so bored that I began to look here and there in the book for topics I already knew or knew I should know something about. _And it is as such, as a handbook, t h a t this volume should be treated: the t e x t does cover a substantial material supported b y a large number of 607