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Published in:
2016 | OriginalPaper | Chapter
Comparison Theorems
Author : Davar Khoshnevisan
Published in: From Lévy-Type Processes to Parabolic SPDEs
Publisher: Springer International Publishing
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In this chapter we outline very briefly some of the main applications of the invariance principle from the preceding chapter. More specifically, we plan to prove that for a large family of SPDEs: (1) the solution is always positive as long as the initial value is positive; and (2) one can sometimes compute “moment functionals” of solutions to various SPDEs to one another. The material of this chapter is borrowed from Joseph–Khoshnevisan–Mueller [30].