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 Dec 22 comment Ito integral via simple process when the integrand is C^1 Have you tried to integrate by parts or equivalently rewriting your integral sum in such a way, that you get increments of $H$? Nov 19 comment Weak convergence $B\circ f_n\to B\circ f$ First, the weak convergence (in the sense of fdd) is clear: just compute the covariance and use the continuity of $f$. For the weak convergence you should use Prokhorov compactness criteria and Garsia-Rodemich-Rumsey inequality (I think, you should additionally assume that function $f$ is Hoelder/Lipschitz continuous ). Jul 2 awarded Curious Oct 17 comment The intersection of linear subspaces is non empty if… I am asking about the intersection of \textbf{hyperspaces} with the inequality!!! sign, rather than the intersection of hyperplanes with the equality sign :) Oct 17 asked The intersection of linear subspaces is non empty if… Mar 18 comment Probability density function of the integral of a continuous stochastic process Are you still interested in this question? Mar 18 asked Negative moments of a functional of Wiener process Dec 30 comment Itô's lemma to solve the SDE Please, specify what is Q. Dec 17 comment Hölder Continuity of Fractional Brownian Motion or for instance, here statslab.cam.ac.uk/~beresty/teach/StoCal/sc3.pdf page 10. Good lecture notes, by the way. Dec 17 comment Hölder Continuity of Fractional Brownian Motion In fact, there Kolmogorov criterion in your formulation can not help apriori. Use this one galton.uchicago.edu/~lalley/Courses/385/GaussianProcesses.pdf on the page six Oct 7 awarded Critic Oct 3 awarded Commentator Oct 3 comment Show that $O_t$ is a Gaussian Process In fact, this Ito integral is for deterministic integrand, hence it coincides with ... .... and by the properties of jointly Gaussian r.v. one gets that $O_t$ is ... ... Sep 23 accepted Convergence to the stable law Sep 23 comment Cylindrical sigma algebra and continuous functions. I do not understand your question. It was just an attempt to refresh some notions in my head. Sep 23 comment Cylindrical sigma algebra and continuous functions. wow! and the same method seems to work when we want to prove that no subset of bounded or measurable functions, for instance, is in $\mathcal B$. Great! Sep 23 accepted Cylindrical sigma algebra and continuous functions. Sep 23 revised Cylindrical sigma algebra and continuous functions. edited body Sep 23 comment Cylindrical sigma algebra and continuous functions. Yes, presicely this. Sep 23 asked Cylindrical sigma algebra and continuous functions.