Tagged: ito

Itô calculus for the rest of us 6

Itô calculus for the rest of us

One of the areas of my research is stochastic differential equations (SDE). I posted about it several times before. One of the things students and collaborators keep asking me about SDEs is the weird stochastic Itô Calculus. Itô Calculus is different from what you learn in 101 calculus. In particular, the chain rule is not longer valid. Let me explain it with...

Introduction to stochastic differential equations 5

Introduction to stochastic differential equations

Stochastic differential equations (SDEs) are basically  inhomogenous ordinary differential equations that depend on an external stochastic process.  Typically, that stochastic process is white noise, which is the mathematical idealization of the noise found in nature. This idealization is handy, because it simplifies the mathematical description. However, this idealization comes at some cost: traditional calculus is no longer valid and you...

Kiyoshi Itô, 93, dies 1

Kiyoshi Itô, 93, dies

November was a rather sad month in the world of stochastic differential equations. In the 26th we were suppose to be celebrating the birth of one of the best mathematicians in history, Norbert Wiener, who gives name to the Wiener process, usually denoted W(t). However, in the 10th, Kiyoshi Itô, the father of stochastic differential equations, passed away. Interestingly both...

Kiyoshi Itô wins the Gauss Prize 0

Kiyoshi Itô wins the Gauss Prize

Kiyoshi Itô (90), professor emeritus at kyoto University, has become the first winner of the Gauss Prize. This prize is to honor scientist whose mathematical research has had an impact outside mathematics. Ito’s work, mainly in establishing a well defined calculus (named Ito’s calculus) to treat high irregular noise functions has got widespread application in describing several stochastic processes across...

Boundary preserving semi-analytical numerical algorithms for stochastic differential equations 0

Boundary preserving semi-analytical numerical algorithms for stochastic differential equations

Esteban Moro and Henri Schurz SIAM Journal of Scientific Computation, Volume 29 Issue 4, Pages 1525-1549 (2007) [pdf]