S. Albeverio, A. Daletskii, E. Lytvynov
Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on 1-forms and associated semigroups are considered. Their probabilistic interpretation is given.
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We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving probability densities.
Verifying the inverse Laplace transform of total expected stock-outs when demand is Poisson
本文验证了需求为 Poisson 的生产库存系统中预期缺货的 Laplace 变换对，阐明了其推导过程并改进了原始结果的准确度。
Laplace Transforms of Stopping Times for Subordinator with Applications to Inventory Control
本文通过亚ordinator的首次通过问题，推导了库存控制中订货时间的拉普拉斯变换，并结合莱维过程理论，提出了一个分析框架，用于解决间歇性需求波动下的库存优化问题。
This paper is devoted to the Depoissonnisation process, which is central in various analyses of the AofA domain. We first recall the two possible paths that may be used in this process. The first path, called here the Depoissonisation path, is better studied and is proven to apply in any practical situation; however, it often uses technical tools, that are not so easy to deal with. Moreover, the various results are scattered in the litterature, and the most recent results are not well known within the AofA domain. The present paper gathers in Section 2 all these results in a survey style. The …
In this article we determine the Laplace transforms of the main boundary functionals of the oscillating compound Poisson process. These are the first passage time of the level, the joint distribution of the first exit time from the interval and the value of the overshoot through the boundary. Under certain conditions we establish the asymptotic behaviour of the mentioned functionals.
Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on forms and associated semigroups are considered. Their probabilistic interpretation is given.
We obtain the state probabilities of various fractional versions of the classical homogeneous Poisson process using an alternate and simpler method known as the Adomian decomposition method (ADM). Generally these state probabilities are obtained by evaluating probability generating function using Laplace transform. A generalization of the space and time fractional Poisson process involving the Caputo type Saigo differential operator is introduced and its state probabilities are obtained using ADM.
The limiting extremal processes of the branching Brownian motion (BBM), the two-speed BBM, and the branching random walk are known to be randomly shifted decorated Poisson point processes (SDPPP). In the proofs of those results, the Laplace functional of the limiting extremal process is shown to satisfy $L[θ_y f]=g(y-τ_f)$ for any nonzero, nonnegative, compactly supported, continuous function $f$, where $θ_y$ is the shift operator, $τ_f$ is a real number that depends on $f$, and $g$ is a real function that is independent of $f$. We show that, under some assumptions, this property characterizes…
Poissonian potential measures for refracted-reflected Lévy processes
研究折射反射谱负Lévy过程在两个独立泊松过程到达时刻的势测度和占据时间拉普拉斯变换，推导出用尺度函数表示的显式表达式。
In this paper we first prove a Clark--Ocone formula for any bounded measurable functional on Poisson space. Then using this formula, under some conditions on the intensity measure of Poisson random measure, we prove a variational representation formula for the Laplace transform of bounded Poisson functionals, which has been conjectured by Dupuis and Ellis [A Weak Convergence Approach to the Theory of Large Deviations (1997) Wiley], p. 122.
Let $(X_t)_{t\geq0}$ be the $n$-dimensional hyperbolic Brownian motion, that is the diffusion on the real hyperbolic space $\D^n$ having the Laplace-Beltrami operator as its generator. The aim of the paper is to derive the formulas for the Gegenbauer transform of the Poisson kernel and the Green function of the ball for the process $(X_t)_{t\geq0}$. Under some additional hypotheses we give the formulas for the Poisson kernel itself. In particular, we provide formulas in $\D^4$ and $\D^6$ spaces for the Poisson kernel and the Green function as well.
We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. Using random walks and exit times, we associate to certain subgraphs (domains) a pair of sequences, each of which is invariant under the action of the automorphism group of the underlying graph. We prove that these invariants differ by an explicit combinatorial factor given by Stirling numbers of the first and second kind. We prove that for any domain with a natural weighting, these invariants determine the eigenvalues of the Laplace operator corresponding to eigenvect…
We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson-Walker space-time. We prove in particular that the Poisson boundary of the diffusion can be identified with the causal boundary of the underlying manifold.
Splitting phenomenon in the Sathe-Selberg theorem, mod-Poisson convergence with auxiliary randomisation and universality of the Gamma factor
本文用辅助随机化揭示的独立性结构，解释多类 mod-Poisson 收敛模型中 Gamma 因子的普适来源，并为 Sathe–Selberg 情形引入 delta-Zeta 分布。
McKean-Vlasov SPDEs driven by Poisson random measure: Well-posedness and large deviation principle
该研究针对泊松随机测度驱动的McKean-Vlasov随机偏微分方程，采用变分框架证明带单调系数的这类方程的适定性与大偏差原理，去掉Gelfand三元组嵌入紧性假设，可应用于有界及无界区域下的拟线性相关方程。
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