walks In 1905 Karl Pearson coined the term random walk while posing a problem describing a random walk on the plane, which was motivated by an application in biology, but such problems involving random walks had already been studied in other fields. Certain gambling problems that were studied centuries earlier can be considered as problems involving random walks. For example, the problem known as the Gambler's ruin is based on a simple random walk, and is an example of a random walk with absorbing barriers. Pascal, Fermat and Huyens all gave numerical solutions to this problem without detailing their methods, and then more detailed solutions were presented by Jakob Bernoulli and Abraham de Moivre. For random walks in -dimensional integer lattices, George Pólya published, in 1919 and 1921, work where he studied the probability of a symmetric random walk returning to a previous position in the lattice. Pólya showed that a symmetric random walk, which has an equal probability to advance in any direction in the lattice, will return to a previous position in the lattice an infinite number of times with probability one in one and two dimensions, but with probability zero in three or higher dimensions. Wiener process The Wiener process or Brownian motion process has its origins in different fields including statistics, finance and physics. In 1880, Thorvald Thiele wrote a paper on the method of least squares, where he used the process to study the errors of a model in time-series analysis. The work is now considered as an early discovery of the statistical method known as Kalman filtering, but the work was largely overlooked. It is thought that the ideas in Thiele's paper were too advanced to have been understood by the broader mathematical and statistical community at the time. The French mathematician Louis Bachelier used a Wiener process in his 1900 thesis in order to model price changes on the Paris Bourse, a stock exchange, without knowing the work of Thiele. It has been speculated that Bachelier drew ideas from the random walk model of Jules Regnault, but Bachelier did not cite him, and Bachelier's thesis is now considered pioneering in the field of financial mathematics. It is commonly thought that Bachelier's work gained little attention and was forgotten for decades until it was rediscovered in the 1950s by the Leonard Savage, and then become more popular after Bachelier's thesis was translated into English