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.
We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.
New rule universally consistent for online learning with non-ergodic data.
Non-ergodic measures found in horocycle flow on Abelian differentials.
The paper explores properties of functions on Teichmüller space, proving theorems about limits and non-ergodicity.
Non-ergodic geodesic flow on Cantor tree surfaces found.
In the paper, we construct conservative Markov processes corresponding to the martingale solutions to the stochastic heat equation on or with values in a general Riemannian maifold, which is only assumed to be complete and stochastic complete. This work is an extension of the previous paper …
Analyzes non-Markovian environments in stochastic approximation.
Strong stability of ergodic iterations proven without ergodic driving sequence.
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loos…
In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant step size for coercive objective functions. For objective functions satisfying a re…
We show that there exists an interval exchange and a point so that the orbit of the point equidistributes for a measure that is not ergodic.
The proximal inertial gradient descent is efficient for the composite minimization and applicable for broad of machine learning problems. In this paper, we revisit the computational complexity of this algorithm and present other novel results, especially on the convergence rates of the objective function values. The no…
We solve the dynamics of the on-line minority game, with general types of decision noise, using generating functional techniques a la De Dominicis and the temporal regularization procedure of Bedeaux et al. The result is a macroscopic dynamical theory in the form of closed equations for correlation- and response functi…
We discuss a variant of Thompson sampling for nonparametric reinforcement learning in a countable classes of general stochastic environments. These environments can be non-Markov, non-ergodic, and partially observable. We show that Thompson sampling learns the environment class in the sense that (1) asymptotically its …
Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a variant of stochastic gradient descent where the random samples are taken on the t…
We consider the problem of dynamic buying and selling of shares from a collection of stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that prices evolve according to an ergodic process with a mild decaying memory proper…
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…
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…
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 …
Sandpile Economics explains how economies can be prone to large crises from small shocks.
Voluntary insurance contracts constitute a puzzle because they increase the expectation value of one party's wealth, whereas both parties must sign for such contracts to exist. Classically, the puzzle is resolved by introducing non-linear utility functions, which encode asymmetric risk preferences; or by assuming the p…
This work tackles large action spaces in RL by binarizing actions.
The study examines dynamics on SU(2)-representation varieties for surfaces and non-orientable surfaces.
This paper addresses metaconsistency in Bayesian inference for metastable systems.
Cooperation is a persistent behavioral pattern of entities pooling and sharing resources. Its ubiquity in nature poses a conundrum. Whenever two entities cooperate, one must willingly relinquish something of value to the other. Why is this apparent altruism favored in evolution? Classical solutions assume a net fitness…
Study shows social reinforcement learning can lead to persistent but metastable polarization.
In this article, I will present a paradox whose purpose is to draw your attention to an important topic in finance, concerning the non-independence of the financial returns (non-ergodic hypothesis). In this paradox, we have two people sitting at a table separated by a black sheet so that they cannot see each other and …
Improves estimation of financial market models using limited data.
In this paper, we consider a framework adapting the notion of cointegration when two asset prices are generated by a driftless Itô-semimartingale featuring jumps with infinite activity, observed regularly and synchronously at high frequency. We develop a regression based estimation of the cointegrated relations method …
Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a domain. Structure learning forms one of the inference challenges of statistical graphi…
U-turn chains improve sampling from complex distributions.
New non-rigid discrete groups found in hyperbolic spaces.
This paper improves convergence bounds for AC and NAC algorithms with function approximation.
Research classifies geometric structures on manifolds using surface group representations.
This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…
We introduce a class of hybrid marked point processes, which encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class amalgamates such existing processes, it also contains novel processes with complex dynamics. These processes are defined implicitly via their intensity and a…
A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.
The study examines Hawkes processes and their long-term behavior.
Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…
We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a G…
Efficient methods for Lévy models using SINH-regular processes.
The aim of process discovery, originating from the area of process mining, is to discover a process model based on business process execution data. A majority of process discovery techniques relies on an event log as an input. An event log is a static source of historical data capturing the execution of a business proc…
GRM uses graph neural networks to score process activity relevance.
Researchers study the geometric properties of a specific type of stable processes.
This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.
The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poiss…
Gaussian process priors are commonly used in aerospace design for performing Bayesian optimization. Nonetheless, Gaussian processes suffer two significant drawbacks: outliers are a priori assumed unlikely, and the posterior variance conditioned on observed data depends only on the locations of those data, not the assoc…