| Summary: | This work uses techniques from convex analysis to study constrained solutions (u, ƞ) to
stochastic differential equations in Hilbert spaces. The process u must stay in the domain of a given
convex function φ, and ƞ is a bounded variation process. The constraint is expressed by a variational
inequality involving u and ƞ, and is equivalent to ƞ ∈∂Փ(u), where Փ(u) = ∫oT(ut)dt.
Both ordinary and partial stochastic differential equations are considered. For ordinary
equations there are minimal restrictions on the constraint function φ. By choosing φ to be
the indicator of a closed convex set, previous results on reflected diffusion processes in finite
dimensions are reproduced.
For stochastic partial differential equations there are severe restrictions on the constraint
functions. Results are obtained if φ is the indicator of a sphere or a halfspace. Other constraint
functions may be possible, subject to a technical condition.
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