## Gheorghe Mihoc's books

The following list of books authored or co-authored by Gheorghe Mihoc is incomplete. However, it still contains 26 items. For a few of the books we have given an extract from a review.
1. (with O Onicescu) La dépendance statistique. Chaînes et familles de chaînes discontinues (1937).

Alex Aitken writes:-

English authors do not seem to have engaged explicitly in the study of Markov chains, though problems of the "random walk", of the mixing of liquids, of molecules under random impacts and the like are instances. ... The tract before us gives a good introduction to Markov chains and a survey of their principal properties. Families of chains, reversibility, stable chains, periodic chains; a secular equation, like that for the modes of a vibrating system (to which the subject has a certain analogy); asymptotic properties; an ergodic principle, to the effect roughly that the probability that a sufficient remote member of the sequence takes the value x depends less and less on a finite number of initial values taken; the tendency to normal distribution of sums of consecutive values; model urn-schemes and other examples; these are some of the topics studied.

2. (with O Onicescu) Probability theory (Romanian) (1939).

3. Treatise on actuarial mathematics (Romanian) (1943).

4. (with O Onicescu) Les chaînes de variables aléatoires. Problemes asymptotiques (1943).

5. An Introduction to the calculus of probability (Romanian) (1954).

6. (with H Ionescu) Mathematics for statisticians and economists (Romanian) (1956).

7. (with O Onicescu and C T Ionescu Tulcea) The calculus of probability and its applications (Romanian) (1956).

There are three parts. The first part is classical. The second, entitled "Stochastic processes", deals with Markov chains, ergodic problems, distributions, limit theorems, time series, aleatory mechanics, and mixing processes. The third part, entitled "Applications", includes statistical mechanics, mathematical statistics, demography and actuarial theory (13 pages are devoted to insurance other than life insurance), and finally there are 6 pages on stellar statistics.

8. (with O Onicescu) Lectures on mathematical statistics (Romanian) (1957).

9. (with V Urseanu) Mathematical applications in statistics (Romanian) (1962).

O Onicescu writes:-

In the present volume the authors give a survey of several mathematical theories in direct connection with their applications in statistics. The achievement of this program may be easily followed in the sequence of the six parts of the book. The first part deals with elements of probability theory; the second is an analysis of statistical distributions, while the third one is devoted to the analysis of time series. The fourth part treats index numbers, the fifth is devoted to sampling theory, and the sixth part to modern methods of statistical calculus.

10. (with H M Ionescu) Mathematical foundations of linear programming (Romanian) (1965).

11. (with M Iosifescu and R Theodorescu) Probability theory and mathematical statistics (Romanian) (1966).

12. (with D Firescu) Mathematical statistics (Romanian) (1966).

13. (with I Nadejde) Mathematical programming (Romanian), 2 Vols (1966-67); Czech translation (1974).

14. (with G Ciucu) Introduction to queueing theory (Romanian) (1967).

R Theodorescu writes:-

This is an introductory text in queueing theory which treats the fundamentals carefully and clearly.

15. (with G Ciucu and V Craiu) The theory of probability and mathematical statistics (Romanian) (1970).

P Holgate explains that this book:-

... devotes a considerable part of its space to laying a firm foundation of mathematical probability theory, and follows this with a section on applications to statistics.

16. (with M Craiu) Statistical inference for dependent variables (Romanian) (1972).

Z Sidak writes:-

The book presents an expository survey of some problems of statistical inference in Markov chains and in chains with complete connections. Its main value is that it gathers in one volume some developments scattered in the literature.

17. (with A Stefanescu) Mathematical programming (Romanian) (1973).

Csaba Fabian writes:-

The authors give an exposition, at a not too advanced mathematical level, of the main types of mathematical programming problems and of the more effective methods for their solution. They begin with a short mathematical introduction and present, in the second chapter, the primal and dual simplex methods and methods for solving transportation problems. Two chapters are devoted to nonlinear programming in special convex and quadratic cases, to discrete programming methods of Gomory and to a quadratic discrete programming method. In the next two chapters they discuss parametric and stochastic programming methods in which only the right hand side and the objective function coefficients are affected. The last chapter deals with dynamic programming. A number of examples serve as illustrations of concrete problems and as numerical illustrations of the methods discussed.

18. (with G Ciucu and A Muja) Mathematical models of queueing theory (Romanian) (1973).

Brian Conolly writes:-

This book is an admirable reference and teaching text on queueing theory. In seven chapters a systematic coverage is given of most of the basic aspects of \$G/G/N\$ systems and of the elementary techniques by which their operational features may be assessed. Some space is given to applications, but the flavour is predominantly theoretical. It is in no way an adverse criticism to write that there is no obviously new material in the presentation

19. (with V Craiu) Treatise on mathematical statistics Vol. 1. Sampling and estimation (Romanian) (1976).

Z Sidak writes:-

This is a textbook for advanced students of statistics, written in a modern purely mathematical style. Its contents are in part non-traditional, including an interesting selection of important older, newer and even very new topics.

20. (with V Craiu) Treatise on mathematical statistics Vol. 2. Testing statistical hypotheses (Romanian) (1977).

21. (with V Urseanu) Sampling and statistical estimation: Theory and applications (Romanian) (1977).

22. (with C Bergthaller and V Urseanu) Stochastic processes: Basic theory and applications (Romanian) (1978).

23. (with V Craiu) Treatise on mathematical statistics Vol. 3. Sequential analysis (Romanian) (1979).

Z Sidak writes:-

The third volume is more specialized; it is devoted solely to sequential analysis. Again, as before, the book is written at an advanced mathematical level and includes some newer and nontraditional material. In addition to general developments, it also contains many examples with specific problem settings and specific distributions.

24. (with V Craiu) Treatise on mathematical statistics Vol. 4. Correlation and linear regression (Romanian) (1981).

25. (with St P Niculescu) Renewal processes (Romanian) (1982).

Gh Oprisan writes:-

This book is a survey of the main theoretical results in renewal theory: classical renewal processes, delayed and stationary renewal processes, renewal theorems for sequences of i.i.d. nonnegative random variables without first or second moments, renewal theorems for nonnegative, but not necessarily identically distributed random variables. The book also contains some results concerning Markov renewal processes and renewal theory in the context of the probability theory in universal semifields.

26. (with V Urseanu and E Ursianu) Statistical analysis (Romanian) (1982).

JOC/EFR March 2011