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Also starting in the 1940s, connections were made between stochastic processes, particularly martingales, and the mathematical field of [[potential theory]], with early ideas by [[Shizuo Kakutani]] and then later work by Joseph Doob.<ref name="Meyer2009"/> Further work, considered pioneering, was done by [[Gilbert Hunt]] in the 1950s, connecting Markov processes and potential theory, which had a significant effect on the theory of Lévy processes and led to more interest in studying Markov processes with methods developed by Itô.<ref name="JarrowProtter2004"/><ref name="Bertoin1998pageVIIIandIX">{{cite book|author=Jean Bertoin|title=Lévy Processes|url=https://books.google.com/books?id=ftcsQgMp5cUC&pg=PR8|year=1998|publisher=Cambridge University Press|isbn=978-0-521-64632-1|page=viii and ix}}</ref><ref name="Steele2012page176">{{cite book|author=J. Michael Steele|title=Stochastic Calculus and Financial Applications|url=https://books.google.com/books?id=fsgkBAAAQBAJ&pg=PR4|year=2012|publisher=Springer Science & Business Media|isbn=978-1-4684-9305-4|page=176}}</ref>

Also starting in the 1940s, connections were made between stochastic processes, particularly martingales, and the mathematical field of [[potential theory]], with early ideas by [[Shizuo Kakutani]] and then later work by Joseph Doob.<ref name="Meyer2009"/> Further work, considered pioneering, was done by [[Gilbert Hunt]] in the 1950s, connecting Markov processes and potential theory, which had a significant effect on the theory of Lévy processes and led to more interest in studying Markov processes with methods developed by Itô.<ref name="JarrowProtter2004"/><ref name="Bertoin1998pageVIIIandIX">{{cite book|author=Jean Bertoin|title=Lévy Processes|url=https://books.google.com/books?id=ftcsQgMp5cUC&pg=PR8|year=1998|publisher=Cambridge University Press|isbn=978-0-521-64632-1|page=viii and ix}}</ref><ref name="Steele2012page176">{{cite book|author=J. Michael Steele|title=Stochastic Calculus and Financial Applications|url=https://books.google.com/books?id=fsgkBAAAQBAJ&pg=PR4|year=2012|publisher=Springer Science & Business Media|isbn=978-1-4684-9305-4|page=176}}</ref>

同样从20世纪40年代开始，随机过程（尤其是鞅）与[[势理论]]的数学领域之间建立了联系，[[Shizuo Kakutani]]的早期思想和Joseph Doob后来的工作。<ref name=“Meyer2009”/>在1950年代[[Gilbert Hunt]]完成了被认为是开创性的进一步工作，把马尔可夫过程和势理论联系起来，这对Lévy过程理论产生了重大影响，并使人们对用It开发的方法研究马尔可夫过程产生了更多的兴趣=https://books.google.com/books？id=ftcsQgMp5cUC&pg=PR8 | year=1998 | publisher=Cambridge University Press | isbn=978-0-521-64632-1 | page=viii and ix}</ref><ref name=“Steele2012page176”{{引用图书|作者=J.Michael Steele | title=随机微积分和金融应用| url=https://books.google.com/books？id=fsgkbaaqbaj&pg=PR4 | year=2012 | publisher=Springer科学与商业媒体| isbn=978-1-4684-9305-4 | page=176}</ref>

同样从20世纪40年代开始，随机过程（尤其是鞅）与[[势理论]]的数学领域之间建立了联系，[[Shizuo Kakutani]]的早期思想和Joseph Doob后来的工作。<ref name=“Meyer2009”/>在1950年代[[Gilbert Hunt]]完成了被认为是开创性的进一步工作，把马尔可夫过程和势理论联系起来，这对Lévy过程理论产生了重大影响，并使人们对用It开发的方法研究马尔可夫过程产生了更多的兴趣<ref name="Bertoin1998pageVIIIandIX">{{cite book|author=Jean Bertoin|title=Lévy Processes|url=https://books.google.com/books？id=ftcsQgMp5cUC&pg=PR8 | year=1998 | publisher=Cambridge University Press | isbn=978-0-521-64632-1 | page=viii and ix}</ref><ref name=“Steele2012page176”{{引用图书|作者=J.Michael Steele | title=随机微积分和金融应用| url=https://books.google.com/books？id=fsgkbaaqbaj&pg=PR4 | year=2012 | publisher=Springer科学与商业媒体| isbn=978-1-4684-9305-4 | page=176}</ref>

In 1953 Doob published his book ''Stochastic processes'', which had a strong influence on the theory of stochastic processes and stressed the importance of measure theory in probability.<ref name="Meyer2009"/>

In 1953 Doob published his book ''Stochastic processes'', which had a strong influence on the theory of stochastic processes and stressed the importance of measure theory in probability.<ref name="Meyer2009"/>

1953年，杜布出版了《随机过程》一书，这本书对随机过程理论产生了重大影响，并强调了测度理论在概率论中的重要性。<ref name=“Meyer2009”/>

953年，杜布出版了《随机过程》一书，这本书对随机过程理论产生了重大影响，并强调了测度理论在概率论中的重要性。<ref name=“Meyer2009”/>

<ref name="Bingham2005">{{cite journal|last1=Bingham|first1=N. H.|title=Doob: a half-century on|journal=Journal of Applied Probability|volume=42|issue=1|year=2005|pages=257–266|issn=0021-9002|doi=10.1239/jap/1110381385|doi-access=free}}</ref> Doob also chiefly developed the theory of martingales, with later substantial contributions by [[Paul-André Meyer]]. Earlier work had been carried out by [[Sergei Bernstein]], [[Paul Lévy (mathematician)|Paul Lévy]] and [[Jean Ville]], the latter adopting the term martingale for the stochastic process.<ref name="HallHeyde2014page1">{{cite book|author1=P. Hall|author2=C. C. Heyde|title=Martingale Limit Theory and Its Application|url=https://books.google.com/books?id=gqriBQAAQBAJ&pg=PR10|year=2014|publisher=Elsevier Science|isbn=978-1-4832-6322-9|pages=1, 2}}</ref><ref name="Dynkin1989">{{cite journal|last1=Dynkin|first1=E. B.|title=Kolmogorov and the Theory of Markov Processes|journal=The Annals of Probability|volume=17|issue=3|year=1989|pages=822–832|issn=0091-1798|doi=10.1214/aop/1176991248|doi-access=free}}</ref> Methods from the theory of martingales became popular for solving various probability problems. Techniques and theory were developed to study Markov processes and then applied to martingales. Conversely, methods from the theory of martingales were established to treat Markov processes.<ref name="Meyer2009"/>

<ref name="Bingham2005">{{cite journal|last1=Bingham|first1=N. H.|title=Doob: a half-century on|journal=Journal of Applied Probability|volume=42|issue=1|year=2005|pages=257–266|issn=0021-9002|doi=10.1239/jap/1110381385|doi-access=free}}</ref> Doob also chiefly developed the theory of martingales, with later substantial contributions by [[Paul-André Meyer]]. Earlier work had been carried out by [[Sergei Bernstein]], [[Paul Lévy (mathematician)|Paul Lévy]] and [[Jean Ville]], the latter adopting the term martingale for the stochastic process.<ref name="HallHeyde2014page1">{{cite book|author1=P. Hall|author2=C. C. Heyde|title=Martingale Limit Theory and Its Application|url=https://books.google.com/books?id=gqriBQAAQBAJ&pg=PR10|year=2014|publisher=Elsevier Science|isbn=978-1-4832-6322-9|pages=1, 2}}</ref><ref name="Dynkin1989">{{cite journal|last1=Dynkin|first1=E. B.|title=Kolmogorov and the Theory of Markov Processes|journal=The Annals of Probability|volume=17|issue=3|year=1989|pages=822–832|issn=0091-1798|doi=10.1214/aop/1176991248|doi-access=free}}</ref> Methods from the theory of martingales became popular for solving various probability problems. Techniques and theory were developed to study Markov processes and then applied to martingales. Conversely, methods from the theory of martingales were established to treat Markov processes.<ref name="Meyer2009"/>

<small>This page was moved from [[wikipedia:en:Stochastic process]]. Its edit history can be viewed at [[随机过程/edithistory]]</small></noinclude>

<small>This page was moved from [[wikipedia:en:Stochastic process]]. Its edit history can be viewed at [[随机过程/edithistory]]</small></noinclude>

[[Category:待整理页面]]

[[Category:待整理页面]]