Tagged: wiener

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 However, this idealization comes at some cost: traditional calculus is no longer valid and you...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...

Writing bad letters of recommendation: the story of Bachelier and Lévy 2

Writing bad letters of recommendation: the story of Bachelier and Lévy

  Take a coin and toss it a number N of times in a time interval of duration T.  Suppose that every time you get head you win a euros and that you lose the same amount of money when you get tail. Then your capital is a random process with ups and dows like this: This process is a stochastic process usually called “Random...