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further enabled the extension of the theory to SDEs of arbitrary form and the identification of the spontaneous BRST supersymmetry breaking as a stochastic generalization of chaos.<ref name=":10">{{Cite journal|last=Ovchinnikov|first=I. V.|date=2016-03-28|title=Introduction to Supersymmetric Theory of Stochastics|journal=Entropy|language=en|volume=18|issue=4|pages=108|doi=10.3390/e18040108|bibcode=2016Entrp..18..108O|arxiv=1511.03393|s2cid=2388285|doi-access=free}}</ref>
In parallel, the concept of the generalized [[transfer operator]] have been introduced in the [[dynamical systems theory]].<ref name=":0">{{cite journal|date=2002|title=Dynamical Zeta Functions and Transfer Operators|url=http://www.ams.org/notices/200208/fea-ruelle.pdf|journal=Notices of the AMS|volume=49|issue=8|pages=887|author=Reulle, D.}}</ref><ref name=":19">{{Cite journal|last=Ruelle|first=D.|date=1990-12-01|title=An extension of the theory of Fredholm determinants|journal=Publications Mathématiques de l'Institut des Hautes Études Scientifiques|language=en|volume=72|issue=1|pages=175–193|doi=10.1007/bf02699133|s2cid=121869096|issn=0073-8301|url=http://www.numdam.org/item/PMIHES_1990__72__175_0/}}</ref> This concept underlies the stochastic evolution operator of STS and provides it with a solid and natural mathematical meaning. Similar constructions were studied in the theory of SDEs.<ref>{{Cite book|title=Stochastic differential geometry at Saint-Flour|last1=Ancona|first1=A.|last2=Elworthy|first2=K. D.|last3=Emery|first3=M.|last4=Kunita|first4=H.|date=2013|publisher=Springer|isbn=9783642341700|oclc=811000422}}</ref><ref>{{Cite book|title=Stochastic flows and stochastic differential equations|last=Kunita|first=H.|date=1997|publisher=Cambridge University Press|isbn=978-0521599252|oclc=36864963}}</ref>
The Parisi-Sourlas method has been recognized <ref name=":Baulieu_Grossman"/><ref name=":1"/> as a member of Witten-type or cohomological [[topological quantum field theory|topological field theory]],<ref name=":3">{{Cite journal|last1=Birmingham|first1=D|last2=Blau|first2=M.|last3=Rakowski|first3=M.|last4=Thompson|first4=G.|title=Topological field theory|journal=Physics Reports|language=en|volume=209|issue=4–5|pages=129–340|doi=10.1016/0370-1573(91)90117-5|year=1991|bibcode=1991PhR...209..129B|url=https://cds.cern.ch/record/218572}}
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