Stochastic equation on compact groups in discrete negative time

Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all solutions in terms of the law of the driving noise.

Strong solutions of Tsirelson's equation in discrete time taking values in compact spaces with semigroup action

Under the assumption that the infinite product of evolution process converges almost surely, the set of strong solutions are characterized by a compact space, which may be regarded as the set of possible initial states.

众数附近的经典离散律：负二项分布与超几何分布的完全局部展开

The classical discrete laws near the mode: complete local expansions for the negative binomial and hypergeometric distributions

该研究推导了负二项分布与超几何分布在众数附近的完全局部渐近展开，补充了二项分布的相关结果，明确了系数形式与众数规则，为离散分布的局部渐近分析提供了完善。

Dynamic programming for discrete-time finite horizon optimal switching problems with negative switching costs

This paper studies a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward and signed (positive and negative) switching costs. Using the martingale approach to optimal stopping problems, we extend a well known explicit dynamic programming method for computing the value function and the optimal strategy to the case of signed switching costs.

Negative Binomial Construction of Random Discrete Distributions on the Infinite Simplex

The Poisson-Kingman distributions, $\mathrm{PK}(ρ)$, on the infinite simplex, can be constructed from a Poisson point process having intensity density $ρ$ or by taking the ranked jumps up till a specified time of a subordinator with Lévy density $ρ$, as proportions of the subordinator. As a natural extension, we replace the Poisson point process with a negative binomial point process having parameter $r>0$ and Lévy density $ρ$, thereby defining a new class $\mathrm{PK}^{(r)}(ρ)$ of distributions on the infinite simplex. The new class contains the two-parameter generalisation $\mathrm{PD}(α, θ)…

The discrete Gaussian free field on a compact manifold

In this article we aim at defining the discrete Gaussian free field (DGFF) on a compact manifold. Since there is no canonical grid approximation of a manifold, we construct a random graph that suitably replaces the square lattice $\mathbb{Z}^d$ in Euclidean space, and prove that the scaling limit of the DGFF is given by the manifold continuum Gaussian free field (GFF). Furthermore using Voronoi tessellations we can interpret the DGFF as element of a Sobolev space and show convergence to the GFF in law with respect to the strong Sobolev topology.