Kalyanapuram Rangachari Parthasarathy (born 25 June 1936) is professor emeritus at the Indian Statistical Institute and a pioneer of quantum stochastic calculus.
He was born in 1936 at Chennai. He studied at the Ramakrishna Mission Vivekananda College, where he completed the B.A. (Honours)
course in Mathematics, and moved to the Indian Statistical Institute, Kolkata, where he completed his Ph.D., under the supervision of C. R. Rao in 1962. He was one of the "famous four" (the others were R. Ranga Rao, Veeravalli S. Varadarajan, and S. R. Srinivasa Varadhan ) in ISI during 1956-1963. He was awarded the first Ph.D. degree of ISI. He received the Shanti Swarup Bhatnagar Prize for Science and Technology in Mathematical Science in 1977 and the TWAS Prize in 1996.
He worked at the Steklov Mathematical Institute, USSR Academy of Sciences (1962–63), as Lecturer where he collaborated with Andrey Kolmogorov. Later he came in United Kingdom as Professor of Statistics in University of Sheffield (1964–68), University of Manchester (1968-70) and later at University of Nottingham where he collaborated with Robin Lyth Hudson on their pioneering work in quantum stochastic calculus. Then he returned to India, and after a few years in Bombay University and the Indian Institute of Technology, Delhi, he came back in 1976 to the new Indian Statistical Institute, Delhi Centre and he stayed there till he retired in 1996.
He is the namesake of Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants along with Bertram Kostant, R. Ranga Rao and Veeravalli S. Varadarajan which they introduced in 1967.
Among the books he has authored are:
- K. R. Parthasarathy. Probability measures on metric spaces. Vol. 352. American Mathematical Soc., 1967.
- Robin Lyth Hudson, and K. R. Parthasarathy. "Quantum Ito's formula and stochastic evolutions." Communications in Mathematical Physics 93.3 (1984): 301-323.
- K. R. Parthasarathy. An introduction to quantum stochastic calculus. Vol. 85. Springer, 1992.
- K. R. Parthasarathy, and Klaus Schmidt. "Positive definite kernels, continuous tensor products, and central limit theorems of probability theory (series: lecture notes in mathematics)." (1972).