Erhan Cinlar

May 28, 1941

Brief Biography

Erhan Cinlar is a Turkish-born probabilist and recipient of the Saul Gass Expository Writing Award. Growing up in Eastern Turkey, Cinlar was  educated in the Franco-European system  of mathematical thought.  He moved to the United States and received all three of his degrees from the University of Michigan. His doctorate, supervised by Ralph Disney, was completed in the university’s industrial engineering department.

 Even though Cinlar’s degrees were in industrial engineering, he began the rare transition from an applied field to abstract theory. His early research was in queueing heory; he noticed the usefulness of Markov renewal processes in queueing theory and started to develop the formal theory of Markov renewal equations and limit theorems. He then applied the new theory to problems in reliability and continuous storage theory, and motivated by those applications, he was led to his development of Markov additive processes and their uses in the theory of continuous regeneration.  Thus he joined the Strasbourg school of probabilists and contributed to the general theory of martingales and Markov processes. His continuing interest in applications lead to his work  on  stochastic models for the reliability of complex materials and dispersion of nutrients in oceans and the attendant theory of stochastic flows.

He received the Saul Gas Expository Writing Award for his book Introduction to Stochastic Processes (1975). The clear writing and elegant notation of the text allowed for it to become the starting point for generations of professionals to learn stochastic processes. In addition to serving as an introductory text, Introduction to Stochastic Processes includes much of Cinlar’s original research, including his important contributions to Poisson processes and Markov renewal theory. His book has withstood the test of time and remains in active use across the globe. His newer book, Probability and Stochastics (2011) is a measure theoretic introduction with new material on martingales, Poisson random measures, Levy processes, Brownian motion, and general Markov processes.

He began a lengthy association with Mathematics of Operations Research, starting as an associate editor, then as the area editor for stochastic processes, and finally as the editor–in-chief. Similarly he was on the editorial boards of Stochastic Processes and Their Applications, Journal of Applied Probability, Advances in Applied Probability. He was named a Fellow of the Institute of Mathematical Statistics in 1974 and a Fellow of the Institute of Operations Research and the Management Sciences in 2003.

Other Biographies

Wikipedia Entry for Erhan Cinlar


University of Michigan, BSE 1963 

University of Michigan, MA 1964 

University of Michigan, PhD 1965 (Mathematics Genealogy


Academic Affiliations

Key Interests in OR/MS

Application Areas

Oral Histories

Erhan Cinlar (1982) Interview by Narahari U. Prabhu. February 28. Ithaca, New York. Eurgene B. Dynkin Collection of Mathematics Interviews. Cornell University: Ithaca, New York. (audio)

Awards and Honors

Institute of Mathematical Statistics Fellow 1974

Institute for Operations Research and the Management Sciences Fellow 2003

Saul Gass Expository Writing Award 2003

President's Award for Distinguished Teaching, Princeton University 2010

Selected Publications

Cinlar E. (1967) Queues with semi-Markovian arrivals. Journal of Applied Probability, 4(2):365-379.

Cinlar E. (1969) Markov renewal theory. Advances in Applied Probability, 1(2): 123-187.

Cinlar E. (1972) Superposition of point processes. , in Lewis P. A. W. ed. Stochastic Point Processes Statistical Analysis, Theory, and Applications. Wiley-Interscience: New York: 549-606.

Cinlar E. (1972) Markov additive processes. Probability Theory and Related Fields, 24(2): 85-93.

Cinlar E. (1973) Theory of continuous storage with Markov additive inputs and a general release rule, Journal of Mathematical Analysis and Applications 43: 207-231.

Cinlar E. (1975) Introduction to Stochastic Processes. Prentice-Hall: New York.

Cinlar E. (1975) Markov renewal theory: A survey. Management Science, 21(7): 727-752.

Bazant Z. P., Cinlar E., & Osman E. (1977) Stochastic process for extrapolating concrete creep. Journal of the Engineering Mechanics Division, 103(6): 1069-1088.

Cinlar E. (1977) Shock and wear models and Markov additive processes. In Theory and Applications of Reliability, I. N. Shimi and C. P. Tsokoseds, Academic Press, New York: 193-214.

Cinlar E. (1980) On a generalization of gamma processes. Journal of Applied Probability, 17(2): 467-480.

Cinlar E. et al (1981)  Semimartingales and Markov processes.  Probability Theory and Related Fields 54: 161-220

Cinlar E. & Zirbel C. L. (1996) Dispersion of particle systems in Brownian flows. Advances in Applied Probability, 34: 53-74.

Cinlar, E. (2011) Probability and Stochastics.  Springer, New York

Additional Resources

Princeton University Operations Research and Financial Engineering. Top Mathematicians Gather to Honor Princeton's Erhan Cinlar. Published April 3, 2006. Accessed May 5, 2015. (link)

Seminar on Stochastic Processes Annual Conference, SSP History. Accessed May 5, 2015. (link)

University of Michigan Industrial and Operations Engineering. Erhan Cinlar receives 2000 IOE Alumni Merit Award. Published January 1, 2002.