White noise space analysis and multiplicative change of measures

@article{Alpay2022WhiteNS,
  title={White noise space analysis and multiplicative change of measures},
  author={Daniel Alpay and Palle E. T. Jorgensen and Motke Porat},
  journal={Journal of Mathematical Physics},
  year={2022}
}
In this paper, we display a family of Gaussian processes, with explicit formulas and transforms. This is presented with the use of duality tools in such a way that the corresponding path-space measures are mutually singular. We make use of a corresponding family of representations of the canonical commutation relations (CCR) in an infinite number of degrees of freedom. A key feature of our construction is explicit formulas for associated transforms; these are infinite-dimensional analogs of… 
View PDF on arXiv

References

SHOWING 1-10 OF 74 REFERENCES
Infinite-dimensional Lie Algebras, Representations, Hermitian Duality and the Operators of Stochastic Calculus
TLDR
The purpose of the paper is to give applications to selected themes at the cross road of operator commutation relations and stochastic calculus, and to use a notion of symmetric (closable) pairs of operators in CCR representation theory.
Spectral Theory for Gaussian Processes: Reproducing Kernels, Boundaries, and L2-Wavelet Generators with Fractional Scales
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions and their reproducing kernels on the one hand, and Gaussian stochastic processes on the…
ITERATED FUNCTION SYSTEMS, REPRESENTATIONS, AND HILBERT SPACE
In this paper, we are concerned with spectral-theoretic features of general iterated function systems (IFS). Such systems arise from the study of iteration limits of a finite family of maps τi,…
A class of Gaussian processes with fractional spectral measures
Spectral theory for Gaussian processes: Reproducing kernels, random functions, boundaries, and $\mathbf L^2$-wavelet generators with fractional scales
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the…
Infinite Product Representations for Kernels and Iterations of Functions
We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new…
On reproducing kernels, and analysis of measures
TLDR
A necessary and sufficient condition for when the measures in the RKHS, and the Hilbert factorizations, are sigma-additive is given, which leads to new insight into the associated Gaussian processes, their Ito calculus and diffusion.
On Free Stochastic Processes and their Derivatives
Asymptotics of Gaussian integrals in infinite dimensions
We introduce an infinite-dimensional version of the classical Laplace method, in its original form, relative to a canonical Gaussian measure associated with a Hilbert space, and for a general phase…
Stochastic Processes Induced by Singular Operators
In this article, we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure σ on ℝ n . The case when σ is assumed absolutely…
...
1
2
3
4
5
...