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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......
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. (
......
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......
Existence and Uniqueness of Invariant Measures for SPDEs with Two Reflecting Walls
Springer Science and Business Media LLC - Tập 27 - Trang 863-877 - 2012
In this article, we study stochastic partial differential equations with two reflecting walls h
1 and h
2, driven by space-time white noise with non-constant diffusion coefficients under periodic boundary conditions. The existence and uniqueness of invariant measures is established under appropriate conditions. The strong Feller property is also obtained.
On the Normalized Laplacian Spectra of Random Geometric Graphs
Springer Science and Business Media LLC - Tập 36 - Trang 46-77 - 2022
In this work, we study the spectrum of the normalized Laplacian and its regularized version for random geometric graphs (RGGs) in various scaling regimes. Two scaling regimes are of special interest, the connectivity and the thermodynamic regime. In the connectivity regime, the average vertex degree grows logarithmically in the graph size or faster. In the thermodynamic regime, the average vertex ......
Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients
Springer Science and Business Media LLC - Tập 35 Số 2 - Trang 1187-1215 - 2022
The multifractal spectrum of statistically self-similar measures
Springer Science and Business Media LLC - Tập 7 Số 3 - Trang 681-702 - 1994
The Length of the Longest Increasing Subsequence of a Random Mallows Permutation
Springer Science and Business Media LLC - Tập 26 - Trang 514-540 - 2011
The Mallows measure on the symmetric group S
n
is the probability measure such that each permutation has probability proportional to q raised to the power of the number of inversions, where q is a positive parameter and the number of inversions of π is equal to the number of pairs i...
Decomposition of Exponential Distributions on Positive Semigroups
Springer Science and Business Media LLC - Tập 19 - Trang 204-220 - 2006
Let (S,·) be a positive semigroup and T a sub-semigroup of S. In many natural cases, an element
$$x\in S$$
can be factored uniquely as x=yz, where
$$y \in T$$
and where z is in an associated “quotient space” S/T. If X has an exponential distribution on S, we show that Y and Z are independent and that Y has an exponential distri......
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