Josef Teichmann
Published 2009-08-19Version 1
In this note we introduce a new approach to rough and stochastic partial differential equations (RPDEs and SPDEs): we consider general Banach spaces as state spaces and -- for the sake of simiplicity -- finite dimensional sources of noise, either rough or stochastic. By means of a time-dependent transformation of state space and rough path theory we are able to construct unique solutions of the respective R- and SPDEs. As a consequence of our construction we can apply the pool of results of rough path theory, in particular we obtain strong and weak numerical schemes of high order converging to the solution process.
A lattice scheme for stochastic partial differential equations of elliptic type in dimension $d\ge 4$
Stationary Solutions of Stochastic Differential Equation with Memory and Stochastic Partial Differential Equations
Rough paths, Signatures and the modelling of functions on streams
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