New, unexpected continuous-time filtrations of sigma-fields, and their properties are treated in

L. Dubins, J. Feldman, M. Smorodinsky, B. Tsirelson, "Decreasing sequences of sigma-fields and a measure change for Brownian motion." Annals of Probability 24:2, 882-904 (1996). [MR97g:60106]

B. Tsirelson, "Triple points: from non-Brownian filtrations to harmonic measures." Geom. and Funct. Anal. 7:6, 1096-1142 (1997). [MR2001g:60199] [download]

These ideas of Vershik remained unknown to western probabilists until the nineties, when they were used [...] by Dubins, Feldman, Smorodinsky and Tsirelson [...] This amazing result triggered new interest to questions on filtrations [...] Shortly thereafter, Tsirelson introduced [...] a new invariant, cosiness [...] These ideas are now diffusing in the community of probabilists, giving rise to a blooming of other works.
(Emery, "On standardness, cosiness and its variants", p. 2.)

There has been much recent interest in Tsirel'son's idea [...] of studying the filtration [...] through the behavior of pairs of such processes.
(Warren, "On the joining of sticky Brownian motion", p. 257. [MR2001c:60132])

Inspired by Anatoly Vershik, I examined new, unexpected continuous products of probability spaces and Hilbert spaces.

B.S. Tsirelson, A.M. Vershik, "Examples of nonlinear continuous tensor products of measure spaces and non-Fock factorizations." Reviews in Mathematical Physics 10:1, 81-145. [MR99c:60085]

See my survey,

B.S. Tsirelson, "Nonclassical stochastic flows and continuous products." Probability Surveys 1, 173-298 (2004) [MR2005m:60080]

See also Chapter 14 "Tsirelson-Vershik product systems" of the book: W. Arveson, "Noncommutative dynamics and E-semigroups." [MR2004g:46082]

The notion of noises has been introduced by B. Tsirelson. [...] An important remark was given by Tsirelson [...] that there exist noises in continuous time which are not isomorphic to classical noises. In particular, he showed the existence of what he calls black noises [...]
(Watanabe, "A simple example of black noise", p. 605. [MR2003a:60069])

The theory of black noises was started by Tsirelson and Vershik in [41]. In particular, they constructed the first examples of zero and one-dimensional black noises (and more of those were found since); we provide the first genuinely two-dimensional example.
(Schramm and Smirnov, "On the scaling limits of planar percolation", p. 1772. [MR2012j:60277])

Citing works

Commutative probability (1994-2010)

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1994       2000                2010

Akahori, Ancona, Barlow, Beghdadi-Sakrani, Benjamini, Bressaud, Buhler, Camia, Coquet, Davini, De Meyer, Donelli, Elworthy, Emery, Eremenko, Evans, Feldman, Fleischmann, Fontes, Fouche, Frei, Freidlin, Garban, Gorbulsky, Hairer, Heicklen, Howitt, Isopi, Izumi, Kalai, Knight, Konstantopoulos, Kulik, Kurtz, Kyprianou, Laurent, Le Jan, Lejay, Leuridan, Li, Maass, Malric, Mansuy, Martinez, Morris, Newman, Nikeghbali, Norris, Ouknine, Pete, Picard, Raimond, Ravishankar, Rubshtein, Salminen, San Martin, Schachermayer, Schweizer, Schertzer, Schramm, Sen, Sheu, Siconolfi, Sirvio, Smorodinsky, Song, Soucaliuc, Sowers, Toth, Turner, Vershik, Warren, Watanabe, Werner, Yor, Zhou. (Detail)

Noncommutative probability (1998-2010)

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           2000                2010

Akahori, Alevras, Arveson, Barreto, Bhat, Floricel, Graev, Gregoratti, Hellmich, Izumi, Jankowski, Jorgensen, Kalai, Koestler, Kuemmerer, Liebscher, Markiewicz, Muhly, Mukherjee, Powers, Price, Skeide, Solel, Speicher, Srinivasan, Tsilevich, Vershik, Vourdas, Watanabe, Yukalov, Zacharias. (Detail)