## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (198.174 recursos)

Electronic Communications in Probability

1. #### A Cramér type moderate deviation theorem for the critical Curie-Weiss model

Can, Van Hao; Pham, Viet-Hung
Limit theorems for the magnetization of Curie-Weiss model have been studied extensively by Ellis and Newman. To refine these results, Chen, Fang and Shao prove Cramér type moderate deviation theorems for non-critical cases by using Stein method. In this paper, we consider the same question for the remaining case - the critical Curie-Weiss model. By direct and simple arguments based on Laplace method, we provide an explicit formula of the error and deduce a Cramér type result.

2. #### Second order behavior of the block counting process of beta coalescents

Lin, Yier; Mallein, Bastien
The Beta coalescents are stochastic processes modeling the genealogy of a population. They appear as the rescaled limits of the genealogical trees of numerous stochastic population models. In this article, we take interest in the number of blocs at small times in the Beta coalescent. Berestycki, Berestycki and Schweinsberg [2] proved a law of large numbers for this quantity. Recently, Limic and Talarczyk [9] proved that a functional central limit theorem holds as well. We give here a simple proof for an unidimensional version of this result, using a coupling between Beta coalescents and continuous-time branching processes.

3. #### Information loss on Gaussian Volterra process

Valdivia, Arturo
Gaussian Volterra processes are processes of the form $(X_{t}:=\int _{\mathbf{T} }k(t,s)\mathrm{d} W_{s})_{t\in \mathbf{T} }$ where $(W_{t})_{t\in \mathbf{T} }$ is Brownian motion, and $k$ is a deterministic Volterra kernel. On integrating the kernel $k$ an information loss may occur, in the sense that the filtration of the Volterra process needs to be enlarged in order to recover the filtration of the driving Brownian motion. In this note we describe such enlargement of filtrations in terms of the Volterra kernel. For kernels of the form $k(t,s)=k(t-s)$ we provide a simple criterion to ensure that the aforementioned filtrations coincide.

4. #### Information loss on Gaussian Volterra process

Valdivia, Arturo
Gaussian Volterra processes are processes of the form $(X_{t}:=\int _{\mathbf{T} }k(t,s)\mathrm{d} W_{s})_{t\in \mathbf{T} }$ where $(W_{t})_{t\in \mathbf{T} }$ is Brownian motion, and $k$ is a deterministic Volterra kernel. On integrating the kernel $k$ an information loss may occur, in the sense that the filtration of the Volterra process needs to be enlarged in order to recover the filtration of the driving Brownian motion. In this note we describe such enlargement of filtrations in terms of the Volterra kernel. For kernels of the form $k(t,s)=k(t-s)$ we provide a simple criterion to ensure that the aforementioned filtrations coincide.

5. #### Note on a one-dimensional system of annihilating particles

We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d. speeds until collision. When two particles collide, they annihilate. We assume the law of speeds to be symmetric. We prove almost sure annihilation of positive-speed particles started from the positive half-line, and existence of a regime of survival of zero-speed particles on the full-line in the case when speeds can only take 3 values. We also state open questions.

6. #### Note on a one-dimensional system of annihilating particles

We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d. speeds until collision. When two particles collide, they annihilate. We assume the law of speeds to be symmetric. We prove almost sure annihilation of positive-speed particles started from the positive half-line, and existence of a regime of survival of zero-speed particles on the full-line in the case when speeds can only take 3 values. We also state open questions.

7. #### Note on a one-dimensional system of annihilating particles

We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d. speeds until collision. When two particles collide, they annihilate. We assume the law of speeds to be symmetric. We prove almost sure annihilation of positive-speed particles started from the positive half-line, and existence of a regime of survival of zero-speed particles on the full-line in the case when speeds can only take 3 values. We also state open questions.

8. #### Note on a one-dimensional system of annihilating particles

We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d. speeds until collision. When two particles collide, they annihilate. We assume the law of speeds to be symmetric. We prove almost sure annihilation of positive-speed particles started from the positive half-line, and existence of a regime of survival of zero-speed particles on the full-line in the case when speeds can only take 3 values. We also state open questions.

9. #### Multidimensional quadratic BSDEs with separated generators

Jamneshan, Asgar; Kupper, Michael; Luo, Peng
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the terminal condition or the dependence in the system are small enough.

10. #### Multidimensional quadratic BSDEs with separated generators

Jamneshan, Asgar; Kupper, Michael; Luo, Peng
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the terminal condition or the dependence in the system are small enough.

11. #### Multidimensional quadratic BSDEs with separated generators

Jamneshan, Asgar; Kupper, Michael; Luo, Peng
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the terminal condition or the dependence in the system are small enough.

12. #### Multidimensional quadratic BSDEs with separated generators

Jamneshan, Asgar; Kupper, Michael; Luo, Peng
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the terminal condition or the dependence in the system are small enough.

13. #### An inequality for the heat kernel on an Abelian Cayley graph

McMurray Price, Thomas
We demonstrate a relationship between the heat kernel on a finite weighted Abelian Cayley graph and Gaussian functions on lattices. This can be used to prove a new inequality for the heat kernel on such a graph: when $t \leq t'$, $\frac{H_t(u, v)} {H_t(u,u)} \leq \frac{H_{t'}(u, v)} {H_{t'}(u,u)}.$ This was an open problem posed by Regev and Shinkar.

14. #### An inequality for the heat kernel on an Abelian Cayley graph

McMurray Price, Thomas
We demonstrate a relationship between the heat kernel on a finite weighted Abelian Cayley graph and Gaussian functions on lattices. This can be used to prove a new inequality for the heat kernel on such a graph: when $t \leq t'$, $\frac{H_t(u, v)} {H_t(u,u)} \leq \frac{H_{t'}(u, v)} {H_{t'}(u,u)}.$ This was an open problem posed by Regev and Shinkar.

15. #### An inequality for the heat kernel on an Abelian Cayley graph

McMurray Price, Thomas
We demonstrate a relationship between the heat kernel on a finite weighted Abelian Cayley graph and Gaussian functions on lattices. This can be used to prove a new inequality for the heat kernel on such a graph: when $t \leq t'$, $\frac{H_t(u, v)} {H_t(u,u)} \leq \frac{H_{t'}(u, v)} {H_{t'}(u,u)}.$ This was an open problem posed by Regev and Shinkar.

16. #### An inequality for the heat kernel on an Abelian Cayley graph

McMurray Price, Thomas
We demonstrate a relationship between the heat kernel on a finite weighted Abelian Cayley graph and Gaussian functions on lattices. This can be used to prove a new inequality for the heat kernel on such a graph: when $t \leq t'$, $\frac{H_t(u, v)} {H_t(u,u)} \leq \frac{H_{t'}(u, v)} {H_{t'}(u,u)}.$ This was an open problem posed by Regev and Shinkar.

17. #### Convergence rates of the random scan Gibbs sampler under the Dobrushin’s uniqueness condition

Wang, Neng-Yi
In this paper, under the Dobrushin’s uniqueness condition, we obtain explicit estimates of the geometrical convergence rate for the random scan Gibbs sampler in the Wasserstein metric.

18. #### Convergence rates of the random scan Gibbs sampler under the Dobrushin’s uniqueness condition

Wang, Neng-Yi
In this paper, under the Dobrushin’s uniqueness condition, we obtain explicit estimates of the geometrical convergence rate for the random scan Gibbs sampler in the Wasserstein metric.

19. #### Convergence rates of the random scan Gibbs sampler under the Dobrushin’s uniqueness condition

Wang, Neng-Yi
In this paper, under the Dobrushin’s uniqueness condition, we obtain explicit estimates of the geometrical convergence rate for the random scan Gibbs sampler in the Wasserstein metric.

20. #### Convergence rates of the random scan Gibbs sampler under the Dobrushin’s uniqueness condition

Wang, Neng-Yi
In this paper, under the Dobrushin’s uniqueness condition, we obtain explicit estimates of the geometrical convergence rate for the random scan Gibbs sampler in the Wasserstein metric.

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