Editing Stochastic process (section)

===Early probability theory===
Probability theory has its origins in games of chance, which have a long history, with some games being played thousands of years ago,<ref name="David1955">{{cite journal|last1=David|first1=F. N.|title=Studies in the History of Probability and Statistics I. Dicing and Gaming (A Note on the History of Probability)|journal=Biometrika|volume=42|issue=1/2|pages=1–15|year=1955|issn=0006-3444|doi=10.2307/2333419|jstor=2333419}}</ref> but very little analysis on them was done in terms of probability.<ref name="Maistrov2014page1">{{cite book|author=L. E. Maistrov|title=Probability Theory: A Historical Sketch|url=https://books.google.com/books?id=2ZbiBQAAQBAJ&pg=PR9|year=2014|publisher=Elsevier Science|isbn=978-1-4832-1863-2|page=1}}</ref> The year 1654 is often considered the birth of probability theory when French mathematicians [[Pierre Fermat]] and [[Blaise Pascal]] had a written correspondence on probability, motivated by a [[Problem of points|gambling problem]].<ref name="Seneta2006page1">{{cite book|author1-link=Eugene Seneta|last1=Seneta|first1=E.|title=Encyclopedia of Statistical Sciences|chapter=Probability, History of|year=2006|doi=10.1002/0471667196.ess2065.pub2|page=1|isbn=978-0471667193}}</ref><ref name="Tabak2014page24to26">{{cite book|author=John Tabak|title=Probability and Statistics: The Science of Uncertainty|url=https://books.google.com/books?id=h3WVqBPHboAC|year=2014|publisher=Infobase Publishing|isbn=978-0-8160-6873-9|pages=24–26}}</ref> But there was earlier mathematical work done on the probability of gambling games such as ''Liber de Ludo Aleae'' by [[Gerolamo Cardano]], written in the 16th century but posthumously published later in 1663.<ref name="Bellhouse2005">{{cite journal|last1=Bellhouse|first1=David|title=Decoding Cardano's Liber de Ludo Aleae|journal=Historia Mathematica|volume=32|issue=2|year=2005|pages=180–202|issn=0315-0860|doi=10.1016/j.hm.2004.04.001|doi-access=free}}</ref>

After Cardano, [[Jakob Bernoulli]]{{efn|Also known as James or Jacques Bernoulli.<ref name="Hald2005page221">{{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=221}}</ref>}} wrote [[Ars Conjectandi]], which is considered a significant event in the history of probability theory. Bernoulli's book was published, also posthumously, in 1713 and inspired many mathematicians to study probability.<ref name="Maistrov2014page56">{{cite book|author=L. E. Maistrov|title=Probability Theory: A Historical Sketch|url=https://books.google.com/books?id=2ZbiBQAAQBAJ&pg=PR9|year=2014|publisher=Elsevier Science|isbn=978-1-4832-1863-2|page=56}}</ref><ref name="Tabak2014page37">{{cite book|author=John Tabak|title=Probability and Statistics: The Science of Uncertainty|url=https://books.google.com/books?id=h3WVqBPHboAC|year=2014|publisher=Infobase Publishing|isbn=978-0-8160-6873-9|page=37}}</ref> But despite some renowned mathematicians contributing to probability theory, such as [[Pierre-Simon Laplace]], [[Abraham de Moivre]], [[Carl Gauss]], [[Siméon Poisson]] and [[Pafnuty Chebyshev]],<ref name="Chung1998">{{cite journal|last1=Chung|first1=Kai Lai|title=Probability and Doob|journal=The American Mathematical Monthly|volume=105|issue=1|pages=28–35|year=1998|issn=0002-9890|doi=10.2307/2589523|jstor=2589523}}</ref><ref name="Bingham2000">{{cite journal|last1=Bingham|first1=N.|title=Studies in the history of probability and statistics XLVI. Measure into probability: from Lebesgue to Kolmogorov|journal=Biometrika|volume=87|issue=1|year=2000|pages=145–156|issn=0006-3444|doi=10.1093/biomet/87.1.145}}</ref> most of the mathematical community{{efn|It has been remarked that a notable exception was the St Petersburg School in Russia, where mathematicians  led by Chebyshev studied probability theory.<ref name="BenziBenzi2007">{{cite journal|last1=Benzi|first1=Margherita|last2=Benzi|first2=Michele|last3=Seneta|first3=Eugene|title=Francesco Paolo Cantelli. b. 20 December 1875 d. 21 July 1966|journal=International Statistical Review|volume=75|issue=2|year=2007|page=128|issn=0306-7734|doi=10.1111/j.1751-5823.2007.00009.x|s2cid=118011380 }}</ref>}} did not consider probability theory to be part of mathematics until the 20th century.<ref name="Chung1998"/><ref name="BenziBenzi2007"/><ref name="Doob1996">{{cite journal|last1=Doob|first1=Joseph L.|title=The Development of Rigor in Mathematical Probability (1900-1950)|journal=The American Mathematical Monthly|volume=103|issue=7|pages=586–595|year=1996|issn=0002-9890|doi=10.2307/2974673|jstor=2974673}}</ref><ref name="Cramer1976">{{cite journal|last1=Cramer|first1=Harald|title=Half a Century with Probability Theory: Some Personal Recollections|journal=The Annals of Probability|volume=4|issue=4|year=1976|pages=509–546|issn=0091-1798|doi=10.1214/aop/1176996025|doi-access=free}}</ref>