| This study develops a bilinear integral and Lebesgue space for operator-valued functions H with respect to an infinite-dimensional measure m, all taking values in abstract locally convex spaces. The integral is then applied to the development of a stochastic integral for general processes H with respect to a square-integrable martingale X.; First, a semivariation is defined in the Banach space setting that more readily lends itself to the construction of a bilinear integral for operator-valued functions. A bilinear integral and Lebesgue space are defined in this context using determining sequences, and is then applied to the setting of the stochastic integral.; Next, a bilinear integral and Lebesgue space, including convergence theorems, are constructed in the more general setting of locally convex space. Under certain assumptions, the bounded measurable functions are integrable. An integral for bounded functions in particular is given through an alternate approach that agrees with the previous integral under the prior assumptions. The spaces L1G and L2G are developed for a locally convex space G.; Finally, a stochastic integral and Lebesgue space are developed for processes H with respect to a square-integrable martingale X in the setting of nuclear locally convex space under certain assumptions. |
