1,721,013 research outputs found
Backward Stochastic Riccati Equations and Infinite Horizon L-Q Optimal Control with Infinite Dimensional State Space and Random Coefficients
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An algorithm for detecting the number of knots in Constrained Principal Component Analysis.
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Young equations with singularities
No full textIn this paper we prove existence and uniqueness of a mild solution to the Young equation dy(t)=Ay(t)dt+σ(y(t))dx(t), t∈[0,T], y(0)=ψ. Here, A is an unbounded operator which generates a semigroup of bounded linear operators (S(t))t≥0 on a Banach space X, x is a real-valued η-Hölder continuous. Our aim is to reduce, in comparison to Gubinelli et al. (2006) and Addona et al. (2022) (see also Deya et al. (2012) and Gubinelli and Tindel, (2010)), the regularity requirement on the initial datum ψ eventually dropping it. The main tool is the definition of a sewing map for a new class of increments which allows the construction of a Young convolution integral in a general interval [a,b]⊂R when the Xα-norm of the function under the integral sign blows up approaching a and Xα is an intermediate space between X and D(A)
Regularity results for non-linear Young equations and applications
Full text linkIn this paper we provide sufficient conditions which ensure that the non-linear equation , , with and being an unbounded operator, admits a unique mild solution such that for any , and we compute the blow-up rate of the norm of as . We stress that the regularity of is independent of the smoothness of the initial datum , which in general does not belong to . As a consequence we get an integral representation of the mild solution which allows us to prove a chain rule formula for smooth functions of
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