Editing Stochastic process (section)

====Random 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.<ref name="Weiss2006page1"/><ref name="Lebowitz1984"/> For example, the problem known as the ''Gambler's ruin'' is based on a simple random walk,<ref name="KarlinTaylor2012page49"/><ref name="Florescu2014page374">{{cite book|author=Ionut Florescu|title=Probability and Stochastic Processes|url=https://books.google.com/books?id=Z5xEBQAAQBAJ&pg=PR22|year=2014|publisher=John Wiley & Sons|isbn=978-1-118-59320-2|pages=374}}</ref> and is an example of a random walk with absorbing barriers.<ref name="Seneta2006page1"/><ref name="Ibe2013page5">{{cite book|author=Oliver C. Ibe|title=Elements of Random Walk and Diffusion Processes|url=https://books.google.com/books?id=DUqaAAAAQBAJ&pg=PT10|year=2013|publisher=John Wiley & Sons|isbn=978-1-118-61793-9|page=5}}</ref> Pascal, Fermat and Huyens all gave numerical solutions to this problem without detailing their methods,<ref name="Hald2005page63">{{cite book|author=Anders Hald|title=A History of Probability and Statistics and Their Applications before 1750|url=https://books.google.com/books?id=pOQy6-qnVx8C|year=2005|publisher=John Wiley & Sons|isbn=978-0-471-72517-6|page=63}}</ref> and then more detailed solutions were presented by Jakob Bernoulli and [[Abraham de Moivre]].<ref name="Hald2005page202">{{cite book|author=Anders Hald|title=A History of Probability and Statistics and Their Applications before 1750|url=https://books.google.com/books?id=pOQy6-qnVx8C|year=2005|publisher=John Wiley & Sons|isbn=978-0-471-72517-6|page=202}}</ref>

For random walks in <math>n</math>-dimensional integer [[Lattice (group)|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.<ref name="Florescu2014page385">{{cite book|author=Ionut Florescu|title=Probability and Stochastic Processes|url=https://books.google.com/books?id=Z5xEBQAAQBAJ&pg=PR22|year=2014|publisher=John Wiley & Sons|isbn=978-1-118-59320-2|pages=385}}</ref><ref name="Hughes1995page111">{{cite book|author=Barry D. Hughes|title=Random Walks and Random Environments: Random walks|url=https://books.google.com/books?id=QhOen_t0LeQC|year=1995|publisher=Clarendon Press|isbn=978-0-19-853788-5|page=111}}</ref>