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Construction of solutions of “structure equations”. (Construction de solutions d’“équations de structure”.) (French) Zbl 0739.60050

Séminaire de probabilités XXIII, Lect. Notes Math. 1372, 142-145 (1989).
[For the entire collection see Zbl 0722.00030.]
The notion of structure equations was introduced by M. Emery, who studied martingales satisfying the equation \[ d[X,X]_ t=dt+\beta X_{t-}dX_ t. \] In this note the author proves the existence of martingales, which satisfy the structure equation \[ d[X,X]_ t=dt+f(X_{t-})dX_ t, \] where \(f\) is an arbitrary continuous function.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras

Citations:

Zbl 0722.00030
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