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最新文章

• Large deviations and mean-field theory for asymmetric random recurrent neural networks AI翻译
  作者：Moynot, O; Samuelides, M
  作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; National Office for Aerospace Studies & Research (ONERA)
  摘要：In this article, we study the asymptotic dynamics of a noisy discrete time neural network, with random asymmetric couplings and thresholds. More precisely, we focus our interest on the limit behaviour of the network when its size grows to infinity with bounded time. In the case of gaussian connection weights, we use the same techniques as Ben Arous and Guionnet (see [3]) to prove that the image law of the distribution of the neurons' activation states by the empirical measure satisfies a tempe...
• Self-repelling walk on the Sierpiniski gasket AI翻译
  作者：Hambly, BM; Hattori, K; Hattori, T
  作者单位：University of Oxford; Shinshu University; Nagoya University
  摘要：We construct a one-parameter family of self-repelling processes on the Sierpinski gasket, by taking continuum limits of self-repelling walks on the pre-Sierpinski gaskets. We prove that our model interpolates between the Brownian motion and the self-avoiding process on the Sierpinski gasket. Namely, we prove that the process is continuous in the parameter in the sense of convergence in law, and that the order of Holder continuity of the sample paths is also continuous in the parameter. We also...
• The genealogy of continuous-state branching processes with immigration AI翻译
  作者：Lambert, A
  作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
  摘要：Recent works by J.F. Le Gall and Y. Le Jan [ 15] have extended the genealogical structure of Galton-Watson processes to continous-state branching processes (CB). We are here interested in processes with immigration (CBI). The height process H which contains all the information about this genealogical structure is defined as a simple local time functional of a strong Markov process X*, called the genealogy-coding process (GCP). We first show its existence using Ito's synthesis theorem. We then ...
• Integration of large-deviation kernels and applications to large deviations for evolutionary games AI翻译
  作者：Finnoff, W
  摘要：We investigate large-deviation properties for systems of probability kernels and these kernels when integrated with respect to a system of measures that also satisfy the large-deviation principle. The results of our analysis are then used to demonstrate the large-deviation property and derive rate functions for systems of measures derived from the distributions of evolutionary game processes.
• Stochastic analysis, rough path analysis and fractional Brownian motions AI翻译
  作者：Coutin, L; Qian, ZM
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：In this paper we show, by using dyadic approximations, the existence of geometric rough path associated with a fractional Brownian motion with Hurst parameter greater than 1/4. Using the integral representation of fractional Brownian motions, we futhermore obtain a Skohorod integral representation of the geometric rough path we constructed. By the results in [Ly1], a stochastic integration theory may be established for fractional Brownian motions, and strong solutions and Wong-Zakai type limit...