120 research outputs found
Interior design of a two-dimensional semiclassic black hole
We look into the inner structure of a two-dimensional dilatonic evaporating
black hole. We establish and employ the homogenous approximation for the
black-hole interior. The field equations admit two types of singularities, and
their local asymptotic structure is investigated. One of these singularities is
found to develop, as a spacelike singularity, inside the black hole. We then
study the internal structure of the evaporating black hole from the horizon to
the singularity.Comment: Typos correcte
Linear stochastic systems: a white noise approach
Using the white noise setting, in particular the Wick product, the Hermite
transform, and the Kondratiev space, we present a new approach to study linear
stochastic systems, where randomness is also included in the transfer function.
We prove BIBO type stability theorems for these systems, both in the discrete
and continuous time cases. We also consider the case of dissipative systems for
both discrete and continuous time systems. We further study -
stability in the discrete time case, and -
stability in the continuous time case
On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions
We present decompositions of various positive kernels as integrals or sums of
positive kernels. Within this framework we study the reproducing kernel Hilbert
spaces associated with the fractional and bi-fractional Brownian motions. As a
tool, we define a new function of two complex variables, which is a natural
generalization of the classical Gamma function for the setting we conside
Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity
We study the internal structure of a two-dimensional dilatonic evaporating
black hole, based on the CGHS model. At the semiclassical level, a (weak)
spacelike singularity was previously found to develop inside the black hole. We
employ here a simplified quantum formulation of spacetime dynamics in the
neighborhood of this singularity, using a minisuperspace-like approach. Quantum
evolution is found to be regular and well-defined at the semiclassical
singularity. A well-localized initial wave-packet propagating towards the
singularity bounces off the latter and retains its well-localized form. Our
simplified quantum treatment thus suggests that spacetime may extend
semiclassically beyond the singularity, and also signifies the specific
extension.Comment: Accepted to Phys. Rev.
On the equivalence of probability spaces
For a general class of Gaussian processes , indexed by a sigma-algebra
of a general measure space , we give
necessary and sufficient conditions for the validity of a quadratic variation
representation for such Gaussian processes, thus recovering , for
, as a quadratic variation of over . We further provide
a harmonic analysis representation for this general class of processes. We
apply these two results to: a computation of generalized Ito-integrals;
and a proof of an explicit, and measure-theoretic equivalence formula,
realizing an equivalence between the two approaches to Gaussian processes, one
where the choice of sample space is the traditional path-space, and the other
where it is Schwartz' space of tempered distributions.Comment: To appear in Journal of Theoretical Probabilit
On the characteristics of a class of Gaussian processes within the white noise space setting
Using the white noise space framework, we define a class of stochastic
processes which include as a particular case the fractional Brownian motion and
its derivative. The covariance functions of these processes are of a special
form, studied by Schoenberg, von Neumann and Krein
Linear Stochastic State Space Theory in the White Noise Space Setting
We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring, and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant, stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system, namely its average behavior
White Noise Based Stochastic Calculus Associated With a Class of Gaussian Processes
Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula
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