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On the Equivalence of Different Approaches to Stochastic Partial Differential Equations
Author(s) -
Jetschke G.
Publication year - 1986
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19861280127
Subject(s) - mathematics , stochastic partial differential equation , white noise , equivalence (formal languages) , partial differential equation , nonlinear system , first order partial differential equation , stochastic differential equation , mathematical analysis , random field , stochastic process , pure mathematics , statistics , physics , quantum mechanics
The solution of a stochastic partial differential equation with white noise disturbance can be treated in two different ways: as a real‐valued random field or as a function‐space valued stochastic process. After introducing these views briefly it is shown that these two approaches are equivalent. Some further results on FOURIER decomposition and on asymptotic behaviour of the linear equation are given and a few comments on the nonlinear case are added.