On April 28, 2026, our teacher, mentor, colleague and friend Murad S. Taqqu passed away at the age of 84. Murad was one of the most influential probabilists and statisticians of his time who almost single-handedly developed the theory of self-similar stochastic processes, laid the groundwork for a systematic analysis of long-range dependent phenomena, and was instrumental in advancing and popularizing heavy-tailed distributions and processes. His work paved the way for a nowadays flourishing field of research, with a wide range of applications across science and engineering. The impact of Murad’s research can also be gauged from the thousands of citations of his publications, and from many books and monographs, by various authors, inspired by his work.
Murad was born on March 21, 1942, in Baghdad into a Jewish family that had lived in Iraq for centuries. In the mid-1940s, wartime anti-Jewish riots drove the Taqqu family to emigrate, first to Lebanon, then to Italy, and finally to Switzerland. It was there that Murad got his school and college education, graduating with a B.Sc. in mathematics and physics from the University of Lausanne. In 1967 Murad became a Ph.D. student at Columbia University in New York, where his mentor was Benoit Mandelbrot, widely recognized as the “father of fractals”. After his graduation in 1972, Murad spent two years as a postdoc in Israel, before moving to Cornell University, where he rose to the rank of full professor. In 1985 Murad moved to Boston University, where he spent the remaining 40 years of his distinguished career, generously supervising, mentoring, and collaborating with scores of researchers.
Murad had a long and productive research career that spanned more than 50 years, during which he published over 260 papers and four research monographs. His work is highly cited; the Web of Science database lists nearly 14,000 citations to Murad’s papers, while Google Scholar counts 9,000 citations of the four books that Murad coauthored. Murad received numerous awards, including a prestigious Guggenheim fellowship, election as a Fellow of the IMS in 1988 as well as of the AMS in 2019, and several best paper prizes. Murad was a much sought-after invited speaker at major conferences and a visiting professor at prestigious institutions all over the world.
Murad made pioneering and lasting contributions to a wide range of topics in probability and statistics. Key themes of his research were long-range dependence, heavy tails, non-central limit theorems and self-similarity. Murad is especially known for his work on long-range dependence, an area that he initiated in the 1970s, and to which he made seminal contributions throughout his entire career. Murad was inspired by ideas of Benoit Mandelbrot who had coined the expression “Joseph effect” after the biblical story of the seven good years followed by seven bad years, which Mandelbrot saw as an example of persistence over a long period that is characteristic for long-range dependence. In providing a rigorous mathematical foundation of the area, Murad investigated stochastic processes that exhibit long-range dependence, proved limit theorems for the analysis of large samples and developed tools for statistical inference of long-range dependent processes, originally all by himself, then soon together with his students and postdocs, and later with an ever-increasing group of coauthors and colleagues from around the world. Among Murad’s lasting contributions is the non-central limit theorem, showing convergence of partial sums of long-range dependent processes to Hermite processes that themselves can be expressed as multiple Wiener–Itô integrals over a Brownian motion process.
In addition to his groundbreaking work on the theoretical foundations of long-range dependent and self-similar processes, Murad also made seminal contributions to their applications in domains such as computer networking, finance, and hydrology. His joint work in the 1990s with his collaborators from Bellcore led to the discovery of the self-similar nature of modern internet traffic and won him several awards, including the 1995 William J. Bennett Prize Paper Award (IEEE Communications Society), the 1996 W.R.G. Baker Prize Award (IEEE Board of Directors), and the 2006 ACM SIGCOMM “Test of Time” Award. The impact of his research in this field is reflected in the more than 20,000 citations listed by Google Scholar.
Murad was a brilliant communicator, both in his writings as well as in his oral presentations, be it talks at conferences or lectures in a classroom. When working on a paper, Murad would not settle for any sentence that was not perfectly formulated nor for any mathematical argument that was not completely clear. He would spend hours with his coauthors going over each line of a paper before it could be submitted. His research monographs Stable Non-Gaussian Random Processes, jointly with Gennady Samorodnitsky, and Long-Range Dependence and Self-Similarity, jointly with Vladas Pipiras, have become highly cited standard references for researchers in these areas.
Murad was a dedicated teacher, Ph.D. advisor, and postdoctoral mentor. His office door was always open, almost every day from early in the morning to late in the afternoon, or even into the evening. You could enter at any time, and Murad would be happy to spend hours discussing your ideas, and he was most generous in sharing his own thoughts. Murad supervised 15 Ph.D. students and mentored several postdocs, many of whom now hold academic positions at prestigious research institutions across the world.
Murad was highly respected in the mathematical community, not only for his pioneering work, but also because of his humanity. He was extremely modest about his own achievements, and at the same time kind and supportive to others. Murad would always talk respectfully about his colleagues, even about the most difficult among them. He was generally soft-spoken and would choose his words carefully. Murad was particularly helpful to scholars in need. In the 1980s, he used his academic network to help refugee scientists from then Eastern Bloc countries to find academic positions in the US. To such causes, Murad devoted much energy.
Murad had broad interests outside of mathematics. He loved languages; in addition to English he spoke Arabic, Hebrew, French, German and Italian. Murad enjoyed reading and travelling. He was an avid photographer who always carried his camera when travelling, both privately and professionally. Above all, Murad was deeply devoted to his family. He was married for nearly 55 years to his beloved wife Rachelle. He was proud of their children Yael and Jonathan, and in later years of their five grandchildren.
The probability and statistics community has lost one of its giants of the past 50 years. We mourn the loss of our teacher, mentor, colleague and friend. But above all, we are deeply grateful for having known Murad, and for the many ways in which he touched and enriched our lives.
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Written by Shuyang Bai, Herold Dehling, Vladas Pipiras, Stilian Stoev, and Walter Willinger, on behalf of all of Murad’s students, friends, colleagues, and collaborators