An application of the Malliavin calculus to infinite dimensional diffusions

Key words and phrases Calculus via regularization, Infinite dimensional analysis, Fractional Brownian motion, Tensor analysis, Clark-Ocone formula, Dirichlet processes, Itˆo

The idea of using Tanaka’s formula to prove Ray–Knight theorems is not new, and can be found for example in Jeulin [8] (for diffusion processes) and in Norris, Rogers and Williams

j : ft -^ F is called Gateaux-analytic, if for any y ' e F', any a e ft and any b e E the function z\^v'of(a-^zb) is a holomorphic functions in one variable on its natural domain

— The collection of locally convex spaces in which the finitely polynomially convex open subsets are domains of holomorphy (resp. domains of existence of holomorphic functions)

Recall the definition of the spectral bound given in (33). Basic reproduction number and spectral bound. Recall that Assumption 0 is in force. Thieme’s result [58, Theorem 3.5]

In [2], we remarked that, projecting at time 0 a general strong Gibbs measure on the path space, the image measure which is obtained on the state space preserves a Gibbsian form in

We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case

Given a random variable F regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and any probability measure with a density