  In the first part of this paper I give the historical background to my
initial interest in stochastic analysis and to the writing of my book
Stochastic Differential Equations. The first edition of this book was published
by Springer in 1985, with the highly appreciated support of Catriona Byrne. In
the second part I present a motivation for modelling the dynamics of a system
subject to a noise by means of a stochastic partial differential equation
(SPDE) driven by a time-space Brownian sheet. This is followed by a brief
survey of time-space white noise and Hida-Malliavin calculus, which are useful
tools for studying such equations. As an illustration I apply white noise
calculus to find an explicit solution of an SPDE describing population growth
in an environment subject to time-space white noise.
