Daniel Ocone
Encyclopedia
Daniel L. Ocone is a Professor in the Mathematics Department at Rutgers University
, where he specializes in probability theory
and stochastic process
es. He obtained his Ph.D at MIT in 1980 under the supervision of Sanjoy K. Mitter
. He is known for the Clark–Ocone theorem. The continuous Ocone martingale is also named after him; it is a continuous martingale
that is conditionally Gaussian, given its quadratic variation
process.
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
, where he specializes in probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
and stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
es. He obtained his Ph.D at MIT in 1980 under the supervision of Sanjoy K. Mitter
Sanjoy K. Mitter
Sanjoy Kumar Mitter is a Professor in the Department of Electrical Engineering and Computer Science at MIT who is a noted control theorist. He has received both the Richard E. Bellman Control Heritage Award from the American Automatic Control Council and the IEEE Control Systems Award...
. He is known for the Clark–Ocone theorem. The continuous Ocone martingale is also named after him; it is a continuous martingale
Martingale (probability theory)
In probability theory, a martingale is a model of a fair game where no knowledge of past events can help to predict future winnings. In particular, a martingale is a sequence of random variables for which, at a particular time in the realized sequence, the expectation of the next value in the...
that is conditionally Gaussian, given its quadratic variation
Quadratic variation
In mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and martingales. Quadratic variation is just one kind of variation of a process.- Definition :...
process.
