Re-figuring Diffy Q

Mar 14, 2011

Kettering's Dr. Leszek Gawarecki and MSU's Vidyadhar Mandrekar have written a systematic study of stochastic differential equations - the foundation of much applied engineering and physics.

When Kettering University's Dr. Leszek Gawarecki, Applied Mathematics Department head, and Michigan State University faculty member Dr. Vidyadhar Mandrekar set out to turn their research into a textbook, the two had a long history on their subject area.

Mandrekar was Gawarecki’s Ph.D. thesis advisor at Michigan State, and their graduate level book, Stochastic Differential Equations in Infinite Dimensions, is a culmination of more than 10 years of research.

“This builds on research we have done for 10 years or more,” Gawarecki said. “Our knowledge of the subject grew and we decided it was time to summarize our findings in a book. Once we started, we realized the subject is complicated and the existing literature is not easily accessible. There was a lot of ‘cleaning’ of the ideas, formulating theorems and proofs. It took a long time to lay the foundations.”

The book is a systematic study of the existence, uniqueness and properties of solutions to stochastic differential equations that arise from practical problems in physics, engineering and finance. The book was released in December of 2010 and fills a significant gap that existed in research on the topic.

“There was a publication that was out in the 1990s that summarized the topic, but 20 years later, it was obsolete,” Gawarecki said. “People who knew we were working on this sometimes grew impatient because they really wanted to use the text.”

Gawarecki has already started writing a second text on the subject.

“It (writing the book) was an incredible learning experience,” he said. “We thought we knew the subject when we started, but we actually only knew about 10 percent of what we know now.”

For more information on the book, visit:  

Contact: Patrick Hayes