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In this section we will apply the Young integral and rough path integral of local time defined in sections 2 and 3 to prove a useful extension to Itˆ o’s formula.. Assume the
But the Malliavin calculus for Gaussian processes can be adapted to it, Skorohod stochastic integrals can be defined, and it will allow us to derive an Itˆ o formula when the
In section 4, we prove a converse to the comparison theorem for BSDEs and then, with the help of this result we study the case when the generators do not depend on the variable y...
Continuous Ocone martingales as weak limits of rescaled martingales. Some invariance properties of the laws of
To prove those results, we use the fact that the ISE has the same distribution (up to a constant scaling) as the total mass of an excursion of the Brownian snake conditioned to have
We will prove that if a limit measure is not absolutely continuous with respect to the Lebesgue measure then the corresponding random walk on the self similar graph does not have
A closed formula for the mean of a maximum likelihood estimator associated with the Brownian bridge is obtained; the exact relation with that of the Brownian motion is
In the following we give a short description of the standard branching random walk, its intrinsic martingales and an associated multiplicative random walk.. Consider a
