Paper shows convergence rates for stochastic processes.
problem Analyzing convergence rates for stochastic processes.
method Quantitative convergence in for Langevin-like processes.
result Iterates converge to an invariant distribution at rate .
On-device research index
arXiv research
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.
169,181 papers · 148 categories
Trend · papers per month
48 results for “Langevin-like processes”
Study of Langevin processes and their convergence rates for non-convex problems.
problem Convergence of Langevin processes and SGD for non-convex optimization problems.
method Quantitative analysis of convergence rates for discrete Langevin-like processes.
result The convergence of SGD for non-convex problems depends on the potential function and additive noise.
Kinetic theory explains financial Brownian motion from trader dynamics.
problem Understanding financial Brownian motion from high-frequency trading dynamics.
method Deriving time-evolution equations, Bogoliubov-Born-Green-Kirkwood-Yvon hierarchies, Boltzmann-like and Langevin-like equations.
result Mathematical foundation for financial Brownian motion parallels physical Brownian motion.
Unified theory of measure-preserving diffusions on manifolds.
problem Deriving a complete recipe for measure-preserving diffusions on manifolds.
method Developed a geometric theory that unifies and generalizes previous constructions, relying on intrinsic geometry of the target measure.
result The completeness result is a direct consequence of manifold topology and target measure geometry.
New sampler tackles complex discrete energy landscapes efficiently.
problem Stagnation in gradient-based discrete samplers for non-convex settings.
method DREXEL sampler with Replica Exchange and Adjusted Metropolis.
result Proves samplers satisfy detailed balance and converge to target distribution.
A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from m…
This work extends score-based methods to binary data on the Boolean hypercube.
problem Learning and sampling binary data on the Boolean hypercube.
method Adopting Bernoulli noise as a smoothing device, deriving a TMF-like expression for the optimal denoiser, and using a Langevin-like sampler.
result The method successfully samples noisy binary data and reduces effective noise through multiple measurements.
A new sampler for complex discrete distributions efficiently updates all variables in parallel.
problem Sampling complex high-dimensional discrete distributions efficiently and accurately.
method Discrete Langevin proposal (DLP) for parallel coordinate updates with controlled stepsize.
result DLP efficiently explores high-dimensional and strongly correlated variables with asymptotic bias of zero for log-quadratic distributions.
GNIs induce asymmetric heavy-tailed noise in SGD, affecting network performance.
problem The effect of Gaussian noise injections on SGD dynamics and network performance.
method Developed a Langevin-like SDE driven by asymmetric heavy-tailed noise to model the modified SGD dynamics.
result GNIs induce an implicit bias that varies with noise heaviness and asymmetry, affecting network performance.
SGD learns sparse parities near computational limits with discontinuous phase transitions.
problem Learning sparse parities in deep learning.
method Empirical and theoretical analysis of SGD on sparse parities.
result SGD makes progress on sparse parities via Fourier gap, not Langevin-like mechanism.
Introduces a new class of hybrid processes combining Markov chains and Hawkes processes.
problem Characterize and ensure existence and uniqueness of complex hybrid marked point processes.
method Defines hybrid marked point processes implicitly via intensity and state process interactions, proving existence and uniqueness under general assumptions.
result Proves existence and uniqueness of hybrid marked point processes, extending existing results.
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…
Deep Neyman-Scott Processesstat.ML
A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.
problem Efficient inference in complex hierarchical point processes.
method Developed an efficient posterior sampling via Markov chain Monte Carlo for likelihood-based inference.
result More hidden Poisson processes improve likelihood fitting and event prediction.
The study examines Hawkes processes and their long-term behavior.
problem Understanding the long-term behavior of Hawkes processes.
method Proving functional limit theorems under various conditions on the dispersion of child events.
result Functional limit theorems hold for Hawkes processes with different levels of child event dispersion.
Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.
problem Need for models with fat tails and computational tractability.
method Represent elliptical distributions as continuous mixtures of Gaussian distributions, derive closed-form expressions for marginal and conditional distributions.
result Elliptical processes offer advantages in robust regression compared to Gaussian processes.
An elementary derivation of the Chinese restaurant process from Sethuraman's stick-breaking processmath.ST
Directly proves CRP from stick-breaking process without measure theory.
problem Indirect proof of CRP from stick-breaking process is complex.
method Direct proof using stick-breaking process to CRP, avoiding measure theory.
result Direct proof connects stick-breaking process to CRP.
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…
SNP extends Neural Processes to handle temporal dependencies in sequences.
problem Handling temporal dependencies in sequences of stochastic processes.
method Integrates a temporal state-transition model into Neural Processes.
result First 4D model capable of dynamic 3D scene modeling.
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.
problem Efficient numerical methods for evaluating Lévy models.
method Defining SL-processes and sSL-processes, deriving properties of characteristic exponent, and showing all popular Lévy processes can be subordinated to Brownian motion.
result All crucial properties of characteristic exponent are consequences of a specific representation, and all popular Lévy processes are SL- or sSL-subordinated Brownian motion.
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…
A Technique for Determining Relevance Scores of Process Activities using Graph-based Neural Networkscs.LG
GRM uses graph neural networks to score process activity relevance.
problem Improving business processes with performance measures.
method Graph Relevance Miner (GRM) based on graph neural networks.
result Quantitatively evaluated relevance scores with four datasets.
Researchers study the geometric properties of a specific type of stable processes.
problem Understanding the information geometry of tempered stable processes.
method Derivation of α-divergence, Fisher information matrices, and α-connections.
result Obtained Fisher information matrices and α-connections for statistical manifolds.
This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.
problem Understanding the relationship between discrete and continuous state spaces in stochastic processes.
method Investigates time-continuous Markov jump processes on discrete state spaces and their correspondence to state-continuous diffusion processes.
result The time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process, bridging discrete and continuous state spaces.
Paper proposes a new method for online process discovery.
problem Online process discovery requires limited memory.
method Mapped online process discovery to cache memory management and applied cache replacement policies.
result Implemented and evaluated a new approach for online process discovery.
Student's-T processes improve on Gaussian processes by handling outliers and variance more flexibly.
problem Outliers and variance limitations in Gaussian processes.
method Generalization of Gaussian processes using Student's-T distribution, with new kernel function and update rule.
result Student's-T processes provide better performance in Bayesian optimization, especially with outliers.
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…
Proposes a new BSP-Tree process for flexible space partition modeling.
problem Limited modelling flexibility of axis-aligned partitions in Mondrian process.
method Introduces a self-consistent Binary Space Partitioning (BSP)-Tree process with oblique cuts.
result Clear inferential improvements over standard Mondrian process and related methods.
Elliptical processes extend Gaussian models with heavier tails.
problem Regression and classification with non-Gaussian likelihoods or heavy tails.
method Spline normalizing flow for variational inference of elliptical distributions.
result Elliptical processes outperform Gaussian processes in non-Gaussian settings.
Recurrent neural networks improve process instance classification.
problem Classifying ongoing process instances based on activities.
method Applied recurrent neural networks, specifically GRU, to classify business process instances.
result GRU outperforms LSTM in training time with similar accuracy.
Ruin Probabilities for Risk Processes with Non-Stationary Arrivals and Subexponential Claimsq-fin.RM
In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary and non-renewal. We give t…
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from cond…
The paper analyzes multivariate Hawkes processes and their induced population processes.
problem Analyzing the time-dependent joint probability distribution of multivariate Hawkes processes.
method Exact and asymptotic analysis of general multivariate Hawkes processes and their induced population processes.
result Full characterization of the time-dependent joint transform of the multivariate population process and its intensity process.
The paper introduces new processes for modeling multivariate volatility.
problem Developing new stochastic processes for multivariate volatility modeling.
method Introducing Volterra Wishart and Volterra pure jump processes with fractional kernels.
result Affine covariance processes for multivariate volatility modeling.
Paper introduces non-linear process convolutions for multi-output Gaussian processes.
problem Building accurate covariance functions for multi-output Gaussian processes.
method Volterra series for non-linearity, closed-form expressions for mean and covariance.
result Non-linear model outperforms classical process convolution in synthetic and real datasets.
New process from fractional BM and OU process yields simpler variance.
problem Simpler model for autocovariance structure.
method Construct new process using fractional BM and OU process, analyze increments.
result Variance of new process easier to compute than FARIMA.
Study on error probability for classification of heavy-tailed renewal processes.
problem Error probability in classification of heavy-tailed renewal processes.
method Asymptotic expressions for Bhattacharyya bound on misclassification error probabilities.
result Obtained asymptotic expressions for misclassification error probabilities.
Study shows convergence rates for BSDEs approximated by compound Poisson processes.
problem Analyzing convergence rates of BSDEs driven by Lévy processes.
method Approximating Lévy processes by compound Poisson processes and studying BSDEs.
result Optimal convergence rates derived for BSDEs in -norm and Wasserstein distance.
Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processescond-mat.stat-mech
Non-Markovian point process shows power-law scaling, similar to nonlinear Markovian process.
problem Understanding the scaling behavior of non-Markovian point processes.
method Analyzed a confined fractional Brownian motion-driven point process and compared it to a nonlinear Markovian process.
result A nonlinear Markovian process can reproduce the power-law scaling behavior of a non-Markovian point process.
Develops Bilateral Gamma processes for financial market modeling.
problem Modeling financial market fluctuations with Lévy processes.
method Exploration of bilateral Gamma distributions and their Lévy processes.
result Validates Bilateral Gamma processes on real financial data.
State spaces of multifactor approximations of nonnegative Volterra processes are linear transformations of the nonnegative orthant.
problem Characterizing state spaces of multifactor approximations of nonnegative Volterra processes.
method Explicit linear transformation of the nonnegative orthant.
result State spaces of multifactor approximations of nonnegative Volterra processes are given by explicit linear transformation of the nonnegative orthant.
The paper models user-advertiser interactions using point processes.
problem Causal inference problems in user-advertiser interaction.
method Temporal marked point processes and neural point processes.
result Neural point processes as practical solutions.
Paper introduces a new model for cyber insurance pricing.
problem Inaccurate pricing of cyber insurance due to multiple, contagious losses.
method Developed a bivariate compound dynamic contagion process.
result Analytical expressions for the compound process and its moments.
The continuum-of-urns scheme, generalized beta and Indian buffet processes, and hierarchies thereofmath.PR
We describe the combinatorial stochastic process underlying a sequence of conditionally independent Bernoulli processes with a shared beta process hazard measure. As shown by Thibaux and Jordan [TJ07], in the special case when the underlying beta process has a constant concentration function and a finite and nonatomic …
New self-exciting random evolutions (SEREs) for modeling traffic and transport processes.
problem Modeling self-exciting and clustering effects in traffic and transport processes.
method Introducing a new process based on a superposition of a Markov chain and a Hawkes process, and constructing self-exciting random evolutions (SEREs).
result Developed new models and limit theorems for SEREs, including averaging and diffusion approximation.
Improved Gaussian process experts model for complex data.
problem Limitations of standard Gaussian processes: scalability and predictive performance.
method Proposes a new mixture model of Gaussian process experts based on kernel stick-breaking processes.
result Improved predictive performance compared to existing models.
Dirac Processes and Default Riskq-fin.PR
We introduce Dirac processes, using Dirac delta functions, for short-rate-type pricing of financial derivatives. Dirac processes add spikes to the existing building blocks of diffusions and jumps. Dirac processes are Generalized Processes, which have not been used directly before because the dollar value of non-Real nu…
Study of Markov-modulated affine processes for richer models in finance.
problem Richer models in various applications.
method Martingale problem approach, characteristic function derivation, mathematical properties study.
result Existence and characteristic function of Markov-modulated affine processes.