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Analog of heat equation for gaussian measure of a ball in Hilberrt space
Springer Science and Business Media LLC - Tập 3 - Trang 563-577 - 1990
If μ a,T is a Gaussian measure on a Hilbert space with meana and covariance
operatorT, andr is a fixed positive number, then the functiong(a,T)=μ a,T {‖x‖...
Mixing Properties of Multivariate Infinitely Divisible Random Fields
Springer Science and Business Media LLC - Tập 32 Số 4 - Trang 1845-1879 - 2019
Tridiagonal Random Matrix: Gaussian Fluctuations and Deviations
Springer Science and Business Media LLC - Tập 30 Số 3 - Trang 1076-1103 - 2017
Occupation Times of General Lévy Processes
Springer Science and Business Media LLC - Tập 30 - Trang 1565-1604 - 2016
For an arbitrary Lévy process X which is not a compound Poisson process, we are
interested in its occupation times. We use a quite novel and useful approach to
derive formulas for the Laplace transform of the joint distribution of X and its
occupation times. Our formulas are compact, and more importantly, the forms of
the formulas clearly demonstrate the essential quantities for the calculation of...
Principles of Large Deviations for the Empirical Processes of the Ornstein–Uhlenbeck Process
Springer Science and Business Media LLC - Tập 12 - Trang 147-179 - 1999
The present paper deals with principles of large deviations for the empirical
processes of the Ornstein–Uhlenbeck process. One such principle due to Donsker
and Varadhan is well known. It uses as underlying space C(ℝ, ℝ d ) endowed with
the topology of uniform convergence on compact sets. The principles of large
deviations proved in the present paper use as underlying spaces appropriate
subspaces ...
Fractional Brownian Density Process and Its Self-Intersection Local Time of Order k
Springer Science and Business Media LLC - Tập 17 - Trang 717-739 - 2004
The fractional Brownian density process is a continuous centered Gaussian $$S$$
′(ℝ d )-valued process which arises as a high-density fluctuation limit of a
Poisson system of independent d-dimensional fractional Brownian motions with
Hurst parameter H. ( $$S$$ ′(ℝ d ) is the space of tempered distributions). The
main result proved in the paper is that if the intensity measure μ of the
(initial) Po...
More on P-Stable Convex Sets in Banach Spaces
Springer Science and Business Media LLC - Tập 13 - Trang 39-64 - 2000
We study the asymptotic behavior and limit distributions for sums S n =bn -1
∑i=1 n ξi,where ξ i, i ≥ 1, are i.i.d. random convex compact (cc) sets in a
given separable Banach space B and summation is defined in a sense of Minkowski.
The following results are obtained: (i) Series (LePage type) and Poisson
integral representations of random stable cc sets in B are established; (ii) The
invariance p...
Mean Residual Life Processes and Associated Submartingales
Springer Science and Business Media LLC - Tập 33 Số 1 - Trang 36-64 - 2020
Some Functional Large Deviations Principles in Nonparametric Function Estimation
Springer Science and Business Media LLC - Tập 25 Số 1 - Trang 280-309 - 2012
In this paper, we investigate functional large deviation behaviors of some
nonparametric function estimates. As a first step, we define a a vector process
W n and study its large deviation behavior in the space L 1×L 1×L 1 with respect
to the weak convergence topology. As by-products, we derive large deviation
principles in the L 1-space equipped with the weak convergence topology
simultaneously f...
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