On recovering solutions for SPDEs from their averages
MetadataShow full item record
We study linear stochastic partial differential equations of parabolic type. We consider a new boundary value problem where a Cauchy condition is replaced by a prescribed average of the solution either over time and probabilistic space for forward SPDEs and over time for backward SPDEs. Well-posedness, existence, uniqueness, and a regularity of the solution for this new problem are obtained. In particular, this can be considered as a possibility to recover a solution of a forward SPDE in a setting where its values at the initial time are unknown, and where the average of the solution over time and probability space is observable, as well as the input processes.
Showing items related by title, author, creator and subject.
Chong, Yen N. (2001)General routing problems deal with transporting some commodities and/or travelling along the axes of a given network in some optimal manner. In the modern world such problems arise in several contexts such as distribution ...
Grigoleit, Mark Ted (2008)The Constrained Shortest Path Problem (CSPP) consists of finding the shortest path in a graph or network that satisfies one or more resource constraints. Without these constraints, the shortest path problem can be solved ...
Awange, Joseph; Fleming, Kevin; Kuhn, Michael; Featherstone, Will; Heck, B.; Anjasmara, Ira (2010)Hydrological monitoring is essential for meaningful water-management policies and actions, especially where water resources are scarce and/or dwindling, as is the case in Australia. In this paper, we investigate the ...