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I will discuss the ergodicity of two kinds of non-stationary processes: random periodic processes and random quasi-periodic processes. I will describe periodic measures, quasi-periodic measures and th...
We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant po...
Conventional inferential methods for (deep) Gaussian Processes models can suffer from high computational complexity as they require large-scale operations with kernel matrices for training and inferen...
We consider a branching process with a random environment, in which the reproduction law of generation $n$ depends on the random environment at time n, unlike a constant distribution assumed in the cl...
Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the dev...
2018年随机过程研讨会(2018 Seminar on Stochastic Processes     2018年  随机过程  研讨会       font style='font-size:12px;'> 2017/12/20
The Seminar on Stochastic Processes 2018 (SSP2018), will be held from May 9 through May 12, 2018 at Brown University, Providence, Rhode Island. From May 9 - 11 the meeting will take place at the Inst...
We establish weak and strong law of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the ...
HIDDEN MARKOV PROCESSES IN THE CONTEXT OF SYMBOLIC DYNAMICS     HIDDEN MARKOV PROCESSES  SYMBOLIC DYNAMICS       font style='font-size:12px;'> 2015/9/29
In an effort to aid communication among different fields and perhaps facilitate progress on problems common toall of them, this article discusses hidden Markov processes from several viewpoints, espec...
LIMIT THEOREMS FOR LOCALLY PERTURBED PLANAR LORENTZ PROCESSES     LOCALLY PERTURBED PLANAR  PROCESSES       font style='font-size:12px;'> 2015/9/29
Modify the scatterer conguration of a planar, nitehorizon Lorentz process in a bounded domain. Sinai asked in 1981 whether for the diffusively scaled variant of the modied process convergence to Bro...
Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDE’s with a small parameter at the second order derivatives are considered in th...
The cutoff phenomenon for ergodic Markov processes     Cutoff phenomenon  ergodic Markov semigroups       font style='font-size:12px;'> 2015/8/26
We consider the cutoff phenomenon in the context of families of ergodic Markov transition functions. This includes classical examples such as families of ergodic finite Markov chains and Brownian mo...
The L2-cutoff for reversible Markov processes     L2-cutoff  Markov semigroups  Normal operators       font style='font-size:12px;'> 2015/8/26
We consider the problem of proving the existence of an L2-cutoff for families of ergodic Markov processes started from given initial distributions and associated with reversible (more, generally, nor...
We derive a large deviation result for the log-likelihood ratio for testing simple hypotheses in locally stationary Gaussian processes. This result allows us to find explicitly the rates of exponentia...
The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left en...

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