arXiv subjects

Jean-Gabriel Attali

Publications and source records attributed to Jean-Gabriel Attali.

7 recordsLinked to original sources

arXiv2026

A Route to Harris ergodicity for Non-Feller Markov Kernels

For non-Feller Markov kernels satisfying a quasi-Feller factorization, the compact-petite-set criterion gives petite compact sets under $ψ$-irreducibility when the support of $ψ$ has non-empty interior. Thus, for coercive Lyapunov functions, the sublevel sets used in the Harris--Lyapunov argument are petite. Under aperiodicity they are small. The Hairer--Mattingly contraction theorem then yields geometric ergodicity in weighted total variation under the usual geometric drift condition.

math.PR↗

arXiv2026

Equilibrium Biphasicity and Non-Binary Pathwise Confinement in Stochastic Ising Models

For the low-temperature two-dimensional Ising model, the two pure Gibbs phases exhaust the extremal equilibrium states, but not the pathwise absorbing structure of the Glauber dynamics. Let \[ P^\pm=\{σ:M_n(σ)\to \pm m_β\},\qquad R=Ω\setminus(P^+\cup P^-). \] We show that $R$ is null under both pure phases but contains a dense pathwise confined subset. More precisely, we construct a dense family of initial configurations whose trajectories are confined to the centered sector \[ C_0=\{σ:M_n(σ)\to0\}\subset R. \] Nevertheless, the corresponding Cesaro averages converge to $\frac12(μ^++μ^-)$. Thus the pathwise absorbing geometry is richer than the Gibbs-phase classification, without creating a third Gibbs phase.

math.PR↗

arXiv2026

Visible absorbing decompositions and uniqueness of invariant probabilities

We identify the measurable absorbing obstruction to uniqueness of invariant probability measures for a Markov kernel. Ordinary absorbing decompositions obstruct global irreducibility and recurrence, but not necessarily uniqueness: an absorbing component may have full mass for no invariant probability. We prove that a Markov kernel has more than one invariant probability if and only if it admits a visible absorbing decomposition, namely two disjoint absorbing sets, each having full mass for an invariant probability. The proof uses only the Jordan decomposition of the difference of two invariant probabilities.

q-fin.MF↗

arXiv2026

Existence and uniqueness of invariant measures for non-Feller Markov semigroups

We study existence and uniqueness of invariant probability measures for continuous-time Markov processes on general state spaces. Existence is obtained from tightness of time averages under a weak regularity assumption inspired by quasi-Feller semigroups, allowing for discontinuous and non-Feller dynamics. Our main contribution concerns uniqueness. Under a natural $ψ$-irreducibility assumption, we show that the normalized resolvent kernel satisfies a domination property with respect to a reference measure. As a consequence, every invariant probability measure charges this reference measure. Since distinct ergodic invariant measures are mutually singular on standard Borel spaces, this domination property implies uniqueness whenever an invariant probability measure exists. The argument is purely measure-theoretic and does not rely on Harris recurrence, return-time estimates, or Foster--Lyapunov conditions, and applies in particular to jump processes and hybrid models with discontinuous dynamics.

math.PR↗

arXiv2026

Asymptotic Stability and Equilibrium Selection in Quasi-Feller Systems with Minimal Moment Conditions

We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in projection-based algorithms, learning in games, and systems with discontinuous decision rules, where classical Feller assumptions and small-noise or large-deviation techniques are not applicable. Under a global Lyapunov condition, we prove that any weak limit of invariant measures must be supported on the set of fixed points of the associated deterministic dynamics. Beyond localization, we establish a sharp exclusion principle for unstable equilibria: strict local maxima and saddle points of the Lyapunov function are shown to carry zero mass in limiting invariant measures under explicit and verifiable non-degeneracy conditions. Our analysis identifies a local mechanism driven by Lyapunov geometry and persistent variance, showing that equilibrium selection in constant-step dynamics is governed by typical fluctuations rather than rare events. These results provide a probabilistic foundation for stability and equilibrium selection in stochastic systems with persistent noise and weak regularity.

math.PR↗

arXiv2026

Analytic Regularity and Approximation Limits of Coefficient-Constrained Shallow Networks

We study approximation limits of single-hidden-layer neural networks with analytic activation functions under global coefficient constraints. Under uniform $\ell^1$ bounds, or more generally sub-exponential growth of the coefficients, we show that such networks generate model classes with strong quantitative regularity, leading to uniform analyticity of the realized functions. As a consequence, up to an exponentially small residual term, the error of best network approximation on generic target functions is bounded from below by the error of best polynomial approximation. In particular, networks with analytic activation functions with controlled coefficients cannot outperform classical polynomial approximation rates on non-analytic targets. The underlying rigidity phenomenon extends to smoother, non-analytic activations satisfying Gevrey-type regularity assumptions, yielding sub-exponential variants of the approximation barrier. The analysis is entirely deterministic and relies on a comparison argument combined with classical Bernstein-type estimates; extensions to higher dimensions are also discussed.

q-fin.MF↗

arXiv2025

A kinetic theory approach to consensus formation in financial markets

It is sometimes acknowledged that (sell-side) equity analysts' recommendations influence investors and therefore market prices. In particular, the S&P 500 is expected to decline (respectively rise) when analysts revise their targets downward (respectively upward). Our findings indicate not only that analysts' consensus exert no influence on market prices, but also that, conversely, analysts appear to set their target prices based on markets prices. Employing a kinetic theory framework, we model the dynamics of analysts' opinions, by taking into account both the mutual influences shaping price consensus and the dynamics of the actual S&P 500 index level. The model is calibrated on a training subset of data and tested on an independent set to assess its predictive power. Our tests show that just three free parameters are enough to accurately predict the one-year average price forecasts of analysts.

math.AP↗