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[18] Trim`eche K., The Dunkl intertwining operator on spaces of functions and distributions and integral repre- sentation of its dual,
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
While a stochastic oscillatory integral with quadratic Wiener functional as phase function has a general representation via Carleman- Fredholm determinant ([3, 6, 10]), in
Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary Itô integral with respect to a Brownian
An important new aspect of the results in [ 12 ] is that they enable one to obtain uniqueness of stationary distributions for stochastic delay differential equations when the
So, using the martingale property of M we see that N is a local martingale. The equivalence between i) and ii) in the above proposition corresponds to a well known
Nualart: Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H in (0,1/2), preprint.. Victoir, Good Rough Path Sequences
Keywords Wiener space, Sobolev space, Stochastic integral, Fractional Brownian Motion, Itˆ o’s formula.. AMS Subject Classification (1991)
