Multiple Wiener-Ito integrals possessing a continuous extension

Large deviations for multiple Wiener-Itô integral processes

“…For the remainder of this subsection, thus, we assume (A Bi E ~i, which is separately a measure in each component; not all multimeasures can be extended to measures on (h,,~~). A more complete account of this concept as well as of the corresponding integration theory may be found in [12] and references therein. We shall just point out the following facts for future use:…”

“…3. (the "adapted case") (A) is assumed and ht = for some h E Multimeasures were considered in [12] in connection with the continuity of scalar multiple Wiener-Ito integrals. In our setup, the regular case provides a LDP by direct application of the contraction principle, but is also instrumental in dealing with the other two cases via an "extended" contraction principle in which the mapping W E Co(~0,1~) --~ Im(h.) E C((0,1~) is allowed to be "approximately" continuous.…”

Multiple fractional integral with Hurst parameter less than 12

“…See, for instance, Johnson and Kallianpur [13] and Sole´and Utzet [19]. We cite also the paper of Nualart and Zakai [16] that considered a multiple Ogawa-type integral, that can be seen as a multiple Stratonovich integral in the sense of Sole´-Utzet and, as the authors pointed out, is the integral closest in spirit to that introduced by Wiener [20].…”

A strong approximation for double subfractional integrals

“…For simplicity we consider only the case of bimeasures and we give a few properties that we need (for more details see [12]). Let X i , B i ð Þ i¼1,2 be two measurable spaces.…”