A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper provides concentration inequalities for Markov chain variance estimators.
Let F be a family of Borel measurable functions on a complete separable metric space. The gap (or fat-shattering) dimension of F is a combinatorial quantity that measures the extent to which functions f in F can separate finite sets of points at a predefined resolution gamma > 0. We establish a connection between the g…
The paper studies harmonic map heat flow to flat tori, proving ergodic behavior and convergence to hyperbolic measure.
New MCMC methods map high-dimensional problems to spheres for better mixing.
New concentration inequality for U-statistics of Markov chains.
AAPI improves regret bound for undiscounted continuing learning in uniformly ergodic MDPs.
This work investigates a mixture of LMC and RMHMC with MMALA for geometric ergodicity.
In the paper portfolio optimization over long run risk sensitive criterion is considered. It is assumed that economic factors which stimulate asset prices are ergodic but non necessarily uniformly ergodic. Solution to suitable Bellman equation using local span contraction with weighted norms is shown. The form of optim…
In this paper long-run risk sensitive optimisation problem is studied with dyadic impulse control applied to continuous-time Feller-Markov process. In contrast to the existing literature, focus is put on unbounded and non-uniformly ergodic case by adapting the weight norm approach. In particular, it is shown how to com…
SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.
We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations with both position-independent and position-dependent integration times. In the former case we find that the conditions for geometric ergodicit…
Recent results on ergodic theory for Riemann surface laminations and foliations.
In this technical note, we adapt an idea of Gabai to construct non-uniquely ergodic, non-geometric, arational trees.
Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A com…
Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for geometric ergodicity of a general class of nonparametric stochastic volatility models with skewness driven by hidden Markov Chain with switching.
We define generalized currents associated with immersions of abstract oriented solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely with immersions of minimal uniquely ergodic solenoids. This makes precise and geo…
We construct an example of a uniquely ergodic measured foliation on a surface such that the associated translation flow on the orientation double cover is minimal but not uniquely ergodic. We then prove a geometric criterion for the horizontal foliation of a quadratic differential to be uniquely ergodic. The second the…
New algorithm detects changes in Markov kernels with unknown post-change kernel.
In [Mas82] and [Vee78] it was proved independently that almost every interval exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem implies that these maps mainly have uniformly distributed orbits. This raises the question under which conditions the orbits yield low-discrepancy sequences. The case o…
We define generalized currents associated with immersions of abstract solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely with immersions of minimal uniquely ergodic solenoids. This makes precise and geometric De…
The paper improves importance sampling and MCMC methods for complex distributions.
This paper compares two NUTS variants and analyzes their convergence and mixing times.
The paper describes decompositions of geometric measures on Anosov homogeneous spaces.
Elliptical slice sampling converges geometrically, providing reliable sampling for Bayesian learning.
The paper proves conditions for non-uniform expansion in partially hyperbolic systems.
We analyze the generalization and robustness of the batched weighted average algorithm for V-geometrically ergodic Markov data. This algorithm is a good alternative to the empirical risk minimization algorithm when the latter suffers from overfitting or when optimizing the empirical risk is hard. For the generalization…
New method detects changes in high-dimensional Markov processes without explicit likelihood evaluation.
Estimates mixing coefficients of geometrically ergodic Markov processes from a single sample path.
The study bounds quantum eigenfunctions on complex manifolds.
We show that the sets in a family with finite VC dimension can be uniformly approximated within a given error by a finite partition. Immediate corollaries include the fact that VC classes have finite bracketing numbers, satisfy uniform laws of averages under strong dependence, and exhibit uniform mixing. Our results ar…
Uniformly perfect Morse boundaries characterize geometric properties of groups.
The paper introduces a new method to create stable ergodic actions on higher-dimensional manifolds.
We construct a counterexample for an analogue of Masur's criterion in the setting of Teichmüller space equipped with the Thurston metric. For that, we find a minimal, filling, non-uniquely ergodic lamination on the seven-times punctured sphere with uniformly bounded annular projection distances. Then we show that a…
Develops Patterson-Sullivan theory for coarse cocycles.
This paper analyzes the convergence of dynamic HMC and NUTS methods.
Study of Matsumoto maps on foliated bundles over hyperbolic manifolds.
We give a simple optimistic algorithm for which it is easy to derive regret bounds of after steps in uniformly ergodic Markov decision processes with states, actions, and mixing time parameter . These bounds are the first regret bounds in the general, non-epi…
We show that for a strongly convergent sequence of geometrically finite Kleinian groups with geometrically finite limit, the Cannon-Thurston maps of limit sets converge uniformly. If however the algebraic and geometric limits differ, as in the well known examples due to Kerckhoff and Thurston, then provided the geometr…
STANLEY improves sampling for complex data models.
This paper addresses metaconsistency in Bayesian inference for metastable systems.
The paper analyzes Q-learning convergence rates with asynchronous updates.
In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered posterior distributions cannot be sampled directly. In this case, the most popular…
New method improves long-term forecasting of stochastic dynamical systems.
Given a n-dimensional lamination endowed with a Riemannian metric, we introduce the notion of a multiplicative cocycle of rank d, where n and d are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, we …
On a compact Kähler manifold there is a canonical action of a Lie-superalgebra on the space of differential forms. It is generated by the differentials, the Lefschetz operator and the adjoints of these operators. We determine the asymptotic distribution of irreducible representations of this Lie-superalgebra on the eig…
Study on measurable pseudo-Anosov maps on surfaces.
Study invariant measures on measured laminations for subgroups of mapping class group.