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.
'Ergodicity economics' is criticized as pseudoscience.
Log-ergodic model improves velocity of money prediction.
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…
This essay discusses the advantages of a probabilistic agent-based approach to questions in theoretical economics, from the nature of economic agents, to the nature of the equilibria supported by their interactions. One idea we propose is that "agents" are meta-individual, hierarchically structured objects, that includ…
Investigates spontaneous symmetry breaking in non-equilibrium systems.
Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require ergodicity in order establish consistency and asymptotic normality of the associat…
Sandpile Economics explains how economies can be prone to large crises from small shocks.
Gambles are random variables that model possible changes in monetary wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but thei…
The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called integration I(d). A class of regression models where cointegration works was identified by Granger and yields the ergodic behavior required for equilibrium expectat…
Study counts ergodic measures in surface lamination strata.
New progress on frame flow ergodicity for nearly pinched manifolds.
Recent results on ergodic theory for Riemann surface laminations and foliations.
Formula connects foliated simplicial volume with group cost.
In this note we show that the Riemann moduli spaces equipped with the Weil--Petersson metric are quantum ergodic for . We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.
We extend to orbifolds classical results on quantum ergodicity due to Shnirelman, Colin de Verdière and Zelditch, proving that, for any positive, first-order self-adjoint elliptic pseudodifferential operator P on a compact orbifold X with positive principal symbol p, ergodicity of the Hamiltonian flow of p implies quan…
Strong stability of ergodic iterations proven without ergodic driving sequence.
The paper studies the ergodicity of frame flow on even-dimensional manifolds.
Non-ergodic measures found in horocycle flow on Abelian differentials.
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 method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.
The study shows that ergodic measures are not generic on non-positively curved manifolds.
We show that Masur's logarithmic law of geodesics in the moduli space of translation surfaces does not imply unique ergodicity of the translation flow, but that a similar law involving the flat systole of a Teichmüller geodesic does imply unique ergodicity. It shows that the flat geometry has a better control on ergodi…
We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is that non-unique ergodicity gives rise to a transverse decomposition of the foldin…
The paper studies ergodicity of flows on subspaces, generalizing earlier work.
A smooth diffeomorphism is said to be distributionally uniquely ergodic (DUE for short) when it is uniquely ergodic and its unique invariant probability measure is the only invariant distribution (up to multiplication by a constant). Ergodic translations on tori are classical examples of DUE diffeomorphisms. In this ar…
A measured solenoid is a laminated space endowed with a tranversal measure invariant by holonomy, as defined in arXiv:0910.2836. A measured solenoid immersed in a smooth manifold produces a closed current (known as generalized Ruelle-Sullivan current). Uniquely ergodic solenoids are those for which there is a unique (u…
The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.
The paper introduces a new method to create stable ergodic actions on higher-dimensional manifolds.
This work investigates a mixture of LMC and RMHMC with MMALA for geometric ergodicity.
Study shows non-wandering, partially hyperbolic systems are ergodic.
We introduce the concept of solenoid as an abstract laminated space. We do a thorough study of solenoids, leading to the notion of ergodic and uniquely ergodic solenoids. We define generalized currents associated with immersions of oriented solenoids with a transversal measure into smooth manifolds, generalizing Ruelle…
Study shows mapping class group action is ergodic on specific representations.
We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.
Proves Torelli group action is ergodic on Lie group character varieties.
The paper provides a link between ergodic theory and symplectic topology. A classical notion of ergodic theory is a skew product map associated with a loop in a group of transformations. We study skew products which come from loops in the group of Hamiltonian diffeomorphisms of a symplectic manifold. Our main question …
We review some developments on clustering stochastic processes and come with the conclusion that asymptotically consistent clustering algorithms can be obtained when the processes are ergodic and the dissimilarity measure satisfies the triangle inequality. Examples are provided when the processes are distribution ergod…
We study the ergodic properties of compositions of interval exchange transformations and rotations. We show that for any interval exchange transformation T, there is a full measure set of αin [0, 1) so that T composed with R_α is uniquely ergodic, where R_α is rotation by α.
SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.
We investigate the relation between economic growth and equality in a modified version of the agent-based asset exchange model (AEM). The modified model is a driven system that for a range of parameter space is effectively ergodic in the limit of an infinite system. We find that the belief that "a rising tide lifts all…
In this technical note, we adapt an idea of Gabai to construct non-uniquely ergodic, non-geometric, arational trees.
We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic BSDE systems}. Such systems arise naturally as candidate solutions to characterize forward performance processes and their associated optimal trading strategies in a…
We study a phenomenological model for the continuous double auction, equivalent to two independent queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior …
Classifies 3D partially hyperbolic systems, proving ergodicity.
Paper shows ergodicity and irreducibility of mapping class group boundary representation.
In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued integrable functions on a probability space subject to a probability-preserving action of an amenable l.c.s.c. group, where in the…
The paper connects geodesic flows, hyperbolic geodesics, and stable ergodicity.
New rule universally consistent for online learning with non-ergodic data.
Approximate inference algorithm is one of the fundamental research fields in machine learning. The two dominant theoretical inference frameworks in machine learning are variational inference (VI) and Markov chain Monte Carlo (MCMC). However, because of the fundamental limitation in the theory, it is very challenging to…