1,720,970 research outputs found
Space Regularity of Evolution Equations Driven by Rough Paths
No full textIn this paper, we consider the linear evolution equation dy(t)=Ay(t)dt+∑i=1dGiy(t)dxi(t), where A is a closed operator, associated to a semigroup, with good smoothing effects in a Banach space E, x is a nonsmooth Rd-path, which is η-Hölder continuous for some η∈13,12, and Gi (i=1,...,d) is a non-smoothing linear operator on E. We prove that the Cauchy problem associated with the previous equation admits a unique mild solution and we also show that the solution increases the regularity of the initial datum as soon as time evolves. Then, we show that the mild solution is also an integral solution and this allows us to prove an Itô formula
Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems
No full textAbstract
We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over
ℝ
d
{\mathbb{R}^{d}}
and in
L
p
{L^{p}}
-spaces with respect to tight evolution systems of measures. Here, the linear part of the equation is a nonautonomous second-order elliptic operator with unbounded coefficients defined in
I
×
ℝ
d
{I\times\mathbb{R}^{d}}
, (I being a right-halfline).
To the above Cauchy problem we associate a nonlinear evolution operator, which we study in detail, proving some summability improving properties. We also study the stability
of the null solution to the Cauchy problem.</jats:p
Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems
Full text linkWe study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over R^d and in L^p-spaces with respect to tight evolution systems of measures. Here, the linear part of the equation is a nonautonomous second-order elliptic operator with unbounded coefficients defined in I x R^d, (I being a right-halfline). To the above Cauchy problem we associate a nonlinear evolution operator, which we study in detail, proving some summability improving properties. We also study the stability of the null solution to the Cauchy problem
On coupled systems of Kolmogorov equation with applications to stochastic differential games
No full textOn invariant measures associated to weakly coupled systems of Kolmogorov equations
No full textIn this paper, we deal with weakly coupled elliptic systems with unbounded coefficients. We prove the existence and characterize all the systems of invariant measures for the associated semigroup associated C_b(R^d;R^m). We also show some relevant properties of the extension of the semigroup to the L^p-spaces related to systems of invariant measures. Finally, we study the asymptotic behaviour of the semigroup as t tends to infinity
Regarding the domain of non-symmetric and, possibly, degenerate Ornstein--Uhlenbeck operators in separable Banach spaces
Full text linkLet be a separable Banach space and let be a linear,
bounded, non-negative and symmetric operator and let be the infinitesimal generator of a strongly continuous
semigroup of contractions on . We consider the abstract Wiener space
where is a centred non-degenerate
Gaussian measure on with covariance operator defined, at least formally, as
\begin{align*} Q_\infty=\int_0^{+\infty} e^{sA}Qe^{sA^*}ds, \end{align*} and
is the Cameron--Martin space associated to .
Let be the reproducing kernel Hilbert space associated with with
inner product . We assume that the operator extends to a bounded linear operator
which satisfies , where
denotes the identity operator on . Let and be the first and second
order Fr\'echet derivative operators, we denote by and the
closure in of the operators and and by
and and their domains in
, respectively,. Furthermore, we denote by
the closure of the operator and by
its domain in . We
characterize the domain of the operator , associated to the bilinear form
\begin{align*} (u,v)\mapsto-\int_{X}[BD_Hu,D_Hv]_Hd\mu_\infty, \qquad u,v\in
W^{1,2}_H(X,\mu_\infty), \end{align*} in . More precisely,
we prove that coincides, up to an equivalent remorming, with a subspace
of . We stress
that we are able to treat the case when is degenerate and non-symmetric
Lp Maximal regularity for vector-valued Schrödinger operators
Full text linkIn this paper we consider the vector -valued Schr & ouml;dinger operator -Delta + V , where the potential term V is a matrix -valued function whose entries belong to L 1loc ( R d ) and, for every x E R d , V ( x ) is a symmetric and nonnegative definite matrix, with non positive off -diagonal terms and with eigenvalues comparable each other. For this class of potential terms we obtain maximal inequality in L 1 ( R d , R m ). Assuming further that the minimal eigenvalue of V belongs to some reverse H & ouml;lder class of order q E (1, oo) U {oo}, we obtain maximal inequality in L p ( R d , R m ), for p in between 1 and some q, and generation results. (c) 2024 Elsevier Masson SAS. All rights are reserved, including those for text and data mining, AI training, and similar technologies
On coupled systems of Kolmogorov equations with applications to stochastic differential games
Full text linkWe prove that a family of linear bounded evolution operators (G(t,s))t ≥ s ∈ I can be associated, in the space of vector-valued bounded and continuous functions, to a class of systems of elliptic operators with unbounded coefficients defined in I × ℝd (where I is a right-halfline or I =ℝ) all having the same principal part. We establish some continuity and representation properties of (G(t,s))t ≥ s ∈ I and a sufficient condition for the evolution operator to be compact in Cb(ℝd;ℝm). We prove also a uniform weighted gradient estimate and some of its more relevant consequence
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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