Why are "Chak" Equations So-Called?

"Cha-Mo" equations are so-named as they were independently discovered by Sydney Chapman and Andrey Kolmogorov.

They are pivotal equations in the theory of Markovian stochastic processes.

Both Chapman and Kolmogorov were mathematicians, with Chapman doubling up as a notable geophysicist studying, amongst other things, the ozone layer and the magnetosphere.

Programming Stochastic Processes - including HMMs

An excellent course on stochastic processes from Technical University of Denmark is here.

Lecture 12 explains Hidden Markov Models.

A lot of work is done to build the foundations of DTMC and CTMC (discrete- and continuous- time Markov chains).

Another great book on stochastic processes with lots of example applications (e.g. from physics and electrical engineering) is by Emmanuel Parzen at Texas A&M University.

A particularly interesting anecdote from the book is how Einstein's equation involving the Wiener process was used to deduce the Avogadro number from Brownian motion experiments.  The Avogadro number is the number of particles (atoms or molecules) in on mole of a substance.

Knuth Volume 2 (Seminumerical Algorithms) describes the basic stochastic simulation techniques.

Vol2 also contains an unusually deep analysis of Euclid's algorithm to compute gcd(one of the oldest known algorithms) and prime factorisation.

Project Martingale (Java API for Derivatives Pricing)

http://martingale.berlios.de/Martingale.html#code

Sample signatures: public class BrownianMotion extends StochasticProcess; public class DigitalRandomSequence extends LowDiscrepancySequence (methods to compute L2-discrepancy). Utilises JFreeChart created by Object Refinery based ici.

Bonjour, Monsieur Martingale!

Here is a conversation with Joseph ("Joe") Leo Doob, the American mathematician from Ohio famous for his martingale convergence theorems. http://www.dartmouth.edu/~chance/Doob/conversation.html 

What motivated Joe to develop deep results in applied probability? In the interview, Joe reveals it was his desire to convert common probabilistic intuition into mathematics (statements and proofs) that drove him to discover his theorems. 

 The wikipedia entry on martingales is also interesting. Doob's soiree into martingale theory coincided with the Great Depression of 1929. 

Other notable statistical activity at that time included Kolmogorov's axiomatisation of probability in 1933. Read Doob's bio here.