Discussion: View Thread

A colleague's question: Can you recommend books (or other resources) that give a gentle introduction to measure theory or stochastic processes, especially treatments that are geared toward statistics?  By "gentle" I mean at a level that competent master's-level applied statisticians could mostly grasp without a rigorous undergrad mathematics background (e.g., 3 semesters of calculus and 1 of linear algebra, but perhaps not differential equations or real analysis).

Responses to this may also help me personally.  My own exposure to measure theory and stochastic processes was more rigorous than what this person would like -- in fact, it was too difficult for me; I'd probably benefit from softer introductions.


Cheers,

Adam
-------------------------------------------
Adam Hafdahl
Owner & Principal Consultant
ARCH Statistical Consulting, LLC
-------------------------------------------

From my viewpoint, a good coverage of the approach to stochastic processes of value to statisticians is the textbook that I had in graduate school,
 
D. R. Cox and H. D. Miller, The Theory of Stochastic Processes, Methuen & Co. Ltd, 11 New Fetter Lane, London, E.C.4., 1965. 

I have no idea if it's still in print, but I would hope so. (Update: It seems to be available now from CRC Press, or Amazon, etc.)   Measure theory is not used, and from my viewpoint, not necessary for applications.  A little knowledge or familiaritywith or prior exposure to ordindary and partial differential equations and complex analysis is helpful when using this text.

I have used the techniques from this book to set up and solve the system of ordinary differential equations for the first passage time to zero inventory for a stock of repairable systems, assuming exponential distributions to events.  For solving such systems, I used the techniques from

W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 3rd Ed., John Wiley& Sons, New York, 1977.

For solving such systems, you may also want to take a look at the treatment of Jordan forms in my favorite linear algebra text

H. W. Brinkmann and E. A. Klotz, Linear Algebra and Analytic Geometry, Addison-Wesley Publishing Co., Reading, MA, 1971.

Best wishes,

-------------------------------------------

Darwin Poritz, Ph.D.
Statistician, JSC Engineering, Technology, and Science Contract
Aerodyne Industries, LLC, M/S JE77
Crew and Thermal Systems Division (EC)
Johnson Space Center
2101 NASA Parkway
Houston, TX 77058

-------------------------------------------