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Displaying 1 –
20 of
1501
We design a particle interpretation of Feynman-Kac measures on path spaces
based on a backward Markovian representation combined with a traditional
mean field particle interpretation of the flow of their final time
marginals. In contrast to traditional genealogical tree based models, these
new particle algorithms can be used to compute normalized additive
functionals “on-the-fly” as well as their
limiting occupation measures with a given precision degree that does not
depend on the final time horizon.
We...
In this paper we consider the map L defined on the Bergman space [...] of the right half plane [...] .
We deal with the problem
⎧ -Δu = f(x,u) + λg(x,u), in Ω,
⎨ ()
⎩
where Ω ⊂ ℝⁿ is a bounded domain, λ ∈ ℝ, and f,g: Ω×ℝ → ℝ are two Carathéodory functions with f(x,0) = g(x,0) = 0. Under suitable assumptions, we prove that there exists λ* > 0 such that, for each λ ∈ (0,λ*), problem () admits a non-zero, non-negative strong solution such that for all p ≥ 2. Moreover, the function is negative and decreasing in ]0,λ*[, where is the energy functional related to ().
Let be a quasicomplete locally convex Hausdorff space. Let be a locally compact Hausdorff space and let , is continuous and vanishes at infinity be endowed with the supremum norm. Starting with the Borel extension theorem for -valued -additive Baire measures on , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map to be weakly compact.
Let be a -algebra, a compact abelian group, an action of by -automorphisms of the fixed point algebra of and the dense sub-algebra of -finite elements in . Further let be a linear operator from into which commutes with and vanishes on . We prove that is a complete dissipation if and only if is closable and its closure generates a -semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative definite...
The existence of classical solutions for some partial differential equations on tori is shown.
A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.
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