A weak stochastic integral in Banach space with application to a linear stochastic differential equation (Q790532)

In this readable paper the authors study in detail cylindrical stochastic processes in separable Banach spaces. They start with the notion of cylindrical Wiener process \(W_ t\), which may be represented as a weakly convergent sum of independent, real Wiener processes. Similar constructions may be found in \textit{A. Bensoussan}, Filtrage optimal des systèmes linéaires (1971; Zbl 0231.93022), \textit{A. V. Balakrishnan}, Applied functional analysis (1976; Zbl 0333.93051) and \textit{L. Gross}, Proc. 5th Berkeley Sympos. math. Statist. Probab., Univ. Calif. 1965/1966, 2, part 1, 31-42 (1967; Zbl 0187.409). Since the covariance may be a general bounded symmetric operator, the distribution of \(W_ t\) is only a cylinder set measure. They then define an adequate notion of stochastic integral with respect to \(W_ t\) and give a theorem on existence and uniqueness for certain stochastic differential equations with linear drift and state-independent diffusion.