ABSTRACT
In the previous two chapters, suggested by the parabolic and hyperbolic Itoˆ equations, we studied the existence, uniqueness, and asymptotic behavior of solutions to some stochastic evolution equations in a Hilbert space. Even though we have given a number of examples to demonstrate some applications of the general results obtained therein, they are relatively simple. In this chapter we will present several more examples to show a wider range of applicability of the general results. A major source of applications for stochastic partial differential equations comes from statistical physics, in particular, the statistical theory of turbulence in fluid dynamics and the related problems. So most of the examples to be presented are given in this area. Recently we have seen some interesting applications of stochastic PDEs to mathematical finance and population biology. Two examples will be given in these areas. For other applications in biology and systems science, see, e.g., the references [7], [24], [30], and [82].
