231,042 research outputs found
A New Algebra ic Approach to Representation Theorems for (Co)integrated Processes up to the Second Order
The paper establishes a unified representation theorem for (co)integrated processes up to the second order which provides a compact and informative insight into the solution of VAR models with unit roots, and sheds light on the cointegration features of the engendered processes. The theorem is primarily stated by taking a one-lag specification as a reference frame, and it is afterwards extended to cover the case of an arbitrary number of lags via a companion-form based approach. All proofs are obtained by resorting to an innovative and powerful algebraic apparatus tailored to the derivation of the intended results.Unified representation theorem, Cointegration, Orthogonal-complement algebra, Laurent expansion in matrix form
A non-linear Renewal Theorem with stationary and slowly changing perturbations
Non-linear renewal theory is extended to include random walks perturbed by
both a slowly changing sequence and a stationary one. Main results include a
version of the Key Renewal Theorem, a derivation of the limiting distribution
of the excess over a boundary, and an expansion for the expected first passage
time. The formulation is motivated by problems in sequential analysis with
staggered entry, where subjects enter a study at random times.Comment: Published at http://dx.doi.org/10.1214/074921706000000680 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
OPE and a low-energy theorem in QCD-like theories
We verify, both perturbatively and nonperturbatively asymptotically in the
ultraviolet (UV), a special case of a low-energy theorem of the NSVZ type in
QCD-like theories, recently derived in arXiv:1701.07833, that relates the
logarithmic derivative with respect to the gauge coupling, or the logarithmic
derivative with respect to the renormalization-group (RG) invariant scale, of
an -point correlator of local operators in one side to an -point
correlator with the insertion of at zero momentum in the other side.
Our computation involves the operator product expansion (OPE) of the scalar
glueball operator, , in massless QCD, worked out perturbatively in
arXiv:1209.1516 -- and in its RG-improved form in the present paper -- by means
of which we extract both the perturbative divergences and the nonperturbative
UV asymptotics in both sides. We also discuss the role of the contact terms in
the OPE, both finite and divergent, discovered some years ago in
arXiv:1209.1516, in relation to the low-energy theorem. Besides, working the
other way around by assuming the low-energy theorem for any 2-point correlator
of a multiplicatively renormalizable gauge-invariant operator, we compute in a
massless QCD-like theory the corresponding perturbative OPE to the order of
and nonperturbative asymptotics. The low-energy theorem has a number of
applications: to the renormalization in asymptotically free QCD-like theories,
both perturbatively and nonperturbatively in the large- 't Hooft and
Veneziano expansions, and to the way the open/closed string duality may or may
not be realized in the would-be solution by canonical string theories for
QCD-like theories, both perturbatively and in the 't Hooft large- expansion.
Our computations will also enter further developments based on the low-energy
theorem.Comment: Some arguments extended and minor typos corrected, paper as published
in JHE
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