Ecole d'Ete de Probabilites de Saint-Flour XV-XVII, 1985. 87 by Persi Diaconis, David Elworthy, Hans Föllmer, Edward Nelson,

By Persi Diaconis, David Elworthy, Hans Föllmer, Edward Nelson, George Papanicolaou, Srinivasa R.S. Varadhan, Paul-Louis Hennequin

This quantity includes certain, worked-out notes of six major classes given on the Saint-Flour summer time colleges from 1985 to 1987.

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We write L~ = FA(D)®FA(D), Li = FA(Dm)DFA(Dk), and where~ i is the vacuum vector in FA(D±). The m-compatible conditional expectation ~D from U(h) to U(D) has been constructed by Evans ([Eva] see also [Ba St Wi])as follows: let H denote the injec~m *-morphism from U(h) into U(D) ®B(Li) whose action on generators is given by H(b(f)) = b(Ef)®~' + I®Rm(b+(E±f)) where ~' is the parity operator in FA(D~). 4) Since ~0~ is irreducible in H A , we may extend ~ expectation from B(H k) into B(LA). R. 1 . i.

R. e. T > O . * Work begun when the author was supported by a CNR Visiting completed when supported by an SERC European Fellowship. Professorship and 47 Let Fs(h ) denote symmetric Fock space over h. ) the vacuum vector in Fs(h). g. [BraRo]) that C(h) may be (unbounded) operators on H s via the prescription a(f) = A( I ~ f)®l + I®A+(J~ f) realized as a *-algebra of for f E h where J is an antilinear involution on h satisfying = and ~ takes the form ~(X) = < ~ s x~S>for XeC(h). Let In = {I .....

L. V. SKOHOROD~ The Theory of Stochastic Processes Ir II and III, Springer Verlag, 1974. 93 E. CARLEN, Conservative Diffusions, preprint Princeton University, Physics Department~ January 1984. [20]W. ZHENG, Semi-martingales dans les vari4t4s et m6canique stochastique Nelson, Th~se, Juin 1984, IRMA Strasbourg 235/TE-25. ~I] S. ALBEVERIO, Ph. BLANCHARD, Ph. COMBE, R. HOEGH-KROHN~ R. RODRIGUEZ, ~I. SIRUGUE, M. SIRUGUE-COLLIN, Magnetic Bottles in a Dirty Environment. A Stochastic Model for Radiation Belts, preprint ZIF Bielefeld 54 (1954).

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