Study improves covariance estimation for SGD under Markovian data, matching best rates.
problem Improving covariance estimation for SGD in Markovian data settings.
method Online overlapping batch-means covariance estimator for SGD under Markovian sampling.
result Established convergence rates for covariance estimation under Markovian sampling.
Kernel analog forecasting studied for multiscale systems.
problem Interpreting data-driven predictions in multiscale dynamical systems.
method Kernel analog forecasting methods applied to multiscale systems with varying Markovian closures.
result Guidance provided for interpreting data-driven predictions in practice.
Paper examines constant stepsize in LSA for Markovian data inference.
problem Improving statistical inference with constant stepsize in LSA for Markovian data.
method Established CLT, used averaged LSA iterates, applied Richardson-Romberg extrapolation.
result Constant stepsize leads to better CI coverage, especially with limited data.
Modeling high-frequency order book data with Hawkes-Markovian process.
problem Capturing the dynamics of high-frequency order book events.
method Hawkes process with Markovian baseline intensities, LASSO regularization, and Akaike Information Criteria.
result Effective modeling of order book dynamics with reduced parameter redundancy.
Markovian RNN adapts to nonstationary data using HMM for better time series prediction.
problem Nonstationary sequential data in real-life applications.
method Markovian RNN with HMM for regime switching and end-to-end optimization.
result Significant performance gains over vanilla RNN and Markov Switching ARIMA.
We analyze SA with Markovian data and nonlinear updates, overcoming prior limitations.
problem Analyzing stochastic approximation with Markovian data and nonlinear updates.
method Fine-grained analysis of SA iterates and Markovian data, leveraging smoothness and recurrence properties.
result Established weak convergence and precise asymptotic bias of SA iterates.
Study on bias and extrapolation in LSA with Markovian data, showing bias reduction with Richardson-Romberg extrapolation.
problem Bias in LSA with constant stepsizes and Markovian data.
method Viewing LSA as a Markov chain, proving convergence and bias expansion, and applying Richardson-Romberg extrapolation.
result Bias is proportional to the stepsize up to higher order terms, and Richardson-Romberg extrapolation reduces the bias.
New method for conformal prediction under Markovian data reduces coverage gap.
problem Reducing coverage gap in conformal prediction for Markovian data.
method Split Conformal Prediction method adapted to Markovian data, with K-split CP for improved performance.
result Coverage gap typically scales as √(t_mix * ln(n) / n) for general Markov chains, and can be reduced to t_mix / (n * ln(n)) with K-split CP.
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.
Projects Markovian processes from Itô semimartingales with jumps.
problem Modeling Itô semimartingales with jumps using Markovian projections.
method Construct Markovian projections for Itô semimartingales with jumps using non-local FPKEs.
result Markovian projections match the marginal laws of the original process.
This paper addresses parameter estimation for wave equations with Markovian switching.
problem Parameter estimation for wave equations with abrupt changes.
method Bayesian statistical framework using discrete sparse Bayesian learning.
result Strong performance in parameter estimation for variable coefficient PDEs.
This paper extends Markovian projections to semimartingales with jumps.
problem Extending Markovian projections to semimartingales with jumps.
method Using Markovian projections to match marginal laws of Itô semimartingales with jumps.
result Existence of Markovian projections for Itô semimartingales with jumps.
Paper improves neural ODEs for forecasting non-Markovian processes.
problem Forecasting irregularly observed time series with incomplete data.
method Path-dependent Neural Jump ODEs with signature transform.
result Path-dependent NJ-ODE outperforms original framework in non-Markovian data.
This paper solves the inversion problem for jump processes using Markovian projections.
problem Calibrating jump-diffusion models with both local and stochastic features.
method Inverting Markovian projections for pure jump processes.
result Constructs calibrated local stochastic intensity (LSI) models for credit risk applications.
Study on statistical inference for nonlinear stochastic approximation with Markovian data.
problem Statistical inference for nonlinear stochastic approximation algorithms with Markovian data.
method Established a functional central limit theorem for the partial-sum process of the target parameter estimate, providing asymptotic pivotal statistics for constructing confidence intervals.
result Valid and efficient asymptotic inference method for nonlinear stochastic approximation algorithms with Markovian data.
Analyzes non-Markovian environments in stochastic approximation.
problem Understanding learning mechanisms in non-ergodic, non-Markovian settings.
method Analytic framework for transformer learning and continual learning.
result Proposes a new approach to transformer and continual learning.
Study finds rough volatility models underperform in SPX option pricing.
problem Inconsistency of rough volatility models with SPX option prices.
method Empirical study using SPX options data, comparing rough and Markovian models.
result Rough volatility models with H∈(0,1/2) are inconsistent with SPX smiles, especially at short maturities. Developed scalable Monte Carlo method for VIX option pricing.
problem VIX option pricing in stochastic Volterra rough volatility models with non-Markovian vol-of-vol.
method Infinite dimensional Markovian representation to devise scalable least squares Monte Carlo.
result Efficient VIX option pricing method for generalized models.
Paper introduces PRMs to learn non-Markovian stochastic rewards for reinforcement learning.
problem Lack of structured representation for non-Markovian stochastic rewards in reinforcement learning.
method Introduces probabilistic reward machines (PRMs) and presents an algorithm to learn them from decision processes.
result Algorithm proves correct and convergent for learning PRMs from decision processes.
Extends Hawkes process for flexible residual modeling in point processes.
problem Modeling high-frequency financial data with complex residual distributions.
method Introduces self and mutually exciting point process with discretely Markovian dynamics.
result Flexible residual distributions improve intensity modeling and high-frequency data estimation.
Stochastic differential equation approximation for linear TD(0) under Markovian noise
problem Temporal-difference learning with linear function approximation
method Stochastic differential equation approximation
result Explains the constant-stepsize error floor
Paper establishes convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
problem Analyzing convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
method Novel discretization of the mean ODE of stochastic approximation algorithms using intervals with diminishing length.
result First almost sure convergence rate and maximal concentration bound with exponential tails for contractive stochastic approximation algorithms with Markovian noise.
Paper improves Oja's algorithm for Markovian data streams.
problem Estimating the top eigenvector of a covariance matrix from Markovian data.
method Improves Oja's algorithm for streaming PCA with Markovian dependence.
result First sharp rate for Oja's algorithm on entire data stream, removing sample size dependence.
Unified analytical tool for non-Markovian jump processes.
problem Analyzing history-dependent jump processes with non-Markovian behavior.
method Developed a standard form of master equations using Laplace-space embedding and asymptotic solution.
result Unified analytical toolset for general non-Markovian processes, leading to the GLE approximation.
The paper analyzes covariate shift in nonparametric regression with Markovian data.
problem Covariate shift in regression problems with Markovian data.
method Extension of nonparametric convergence rates to Markovian dependence structures, using Hölder smoothness assumptions and similarity measures.
result Precise convergence rates for Nadaraya-Watson kernel estimators under specific Markovian conditions.
We develop a Markovian approximation for SVV models to compute hedging strategies.
problem Computing optimal hedging strategies for SVV models with non-Markovian noise.
method Develop a Markovian approximation of the Volterra noise kernel to compute hedging strategies.
result Error estimates for the approximation of volatility, prices, and optimal hedge.
A new HOM model improves forecasting of Indian base metal prices.
problem Improving accuracy in predicting base metal prices in the Indian market.
method A Higher Order Markovian (HOM) model with varying order based on market delay.
result The HOM model consistently outperforms the standard Markovian model in forecasting.
Study analyzes non-Markovian effects in financial markets over multiple years.
problem Understanding non-Markovian dynamics and trader interactions in financial markets.
method Empirical analysis of self-response functions and trade sign correlators for different stocks over multiple years.
result Significant variations in traders' interactions over time, indicating changes in market mechanisms.
Describes state variables in sequential decision problems, linking them to Markovian and non-Markovian models.
problem Sequential decision problems, especially in active learning and POMDPs, where decisions affect what is observed and learned.
method Canonical framework and novel two-agent perspective of POMDPs, defining state variables to claim Markovian or non-Markovian models.
result Properly modeled sequential decision problems are Markovian, while real decision problems are often non-Markovian.
Deep learning solves non-Markovian FBSDEs for utility maximization.
problem Solving utility maximization problems under rough volatility.
method Deep learning-based numerical methods for non-Markovian fully coupled FBSDEs.
result Error estimates and convergence provided for the deep learning approach.
Sparse Markovian Gaussian processes improve probabilistic model inference for large datasets.
problem Efficient inference for large-scale time series data.
method Combining inducing variables with Kalman filter-like recursions for linear scaling.
result General site-based approach for approximating non-Gaussian likelihoods.
Study on regression with Markovian data, establishing limits and proposing an improved algorithm.
problem Least squares regression with dependent Markovian data.
method Sharp information theoretic lower bounds, analysis of SGD-DD and SGD, experience replay algorithm.
result Experience replay algorithm outperforms SGD-DD in Markovian data regression.
MER algorithm speeds up VI solving with Markovian data.
problem Solving stochastic variational inequalities with Markovian data.
method MER algorithm using multi-scale sampling from a Markovian buffer.
result Achieves faster convergence without knowing Markov chain mixing time.
Investigates optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
problem Optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
method Martingale optimal principle and quadratic BSDEs with exponential moment.
result Establishes optimal strategies for consumption and investment.
A new method scales Gaussian process variational autoencoders to handle high-dimensional time series.
problem Scalability issue in Gaussian process variational autoencoders (GPVAEs).
method Introducing Markovian GPs and using Kalman filtering and smoothing for linear time training.
result MGPVAE outperforms existing approaches in various tasks with high scalability.
We simplify a complex volatility model to make it easier to price options.
problem The rough Bergomi model's non-Markovian nature complicates option pricing.
method We approximate the rBergomi model with a Bergomi model that is Markovian.
result The rBergomi model can be effectively approximated by a Markovian model.
This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an Itô-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which satisfies the generalized Hamilton-Jacobi-Bellman (HJB) equation with Markovian switching. Then, by using …
The paper develops a deep signature approach for option pricing under non-Markovian stochastic volatility models.
problem Pricing options under non-Markovian stochastic volatility models is challenging due to the dependence on historical paths.
method Reformulate the asset dynamics as a rough stochastic differential equation and represent rough paths via signatures. Apply standard analytical tools to solve the transformed equation.
result The deep signature approach provides a theoretically grounded and computationally efficient framework for option pricing.
The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question …
Improved SGD bounds for machine learning models with Markovian noise.
problem Uniform high-probability bounds for SGD under PL condition with Markovian noise.
method Combining Poisson equation for Markovian noise and probabilistic induction for almost-sure bounds.
result Matching 1/k decay rate for expected suboptimality. Paper derives convergence rates and confidence intervals for LSA with Markovian noise.
problem Analyzing convergence rates and constructing confidence intervals for LSA with Markovian noise.
method Derives non-asymptotic Berry-Esseen bounds and multiplier block bootstrap procedure.
result Provides O(n−1/4) convergence rates and guarantees consistent inference. This paper studies a class of non−Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a Z−constrained BSDE, with dynamics associated to a non singular underlying forward process. Du…
A method for optimizing under unknown Markovian data distributions.
problem Optimizing under unknown and indirectly observed probability distributions via Markovian data.
method Data-driven distributionally robust optimization model with Frank-Wolfe algorithm.
result The proposed method finds a stationary point efficiently and outperforms state-of-the-art methods.
Paper tackles robust offline RL for non-Markovian processes, improving efficiency and applicability.
problem Learning robust policies for non-Markovian decision processes with limited offline data.
method Proposes a novel algorithm with dataset distillation and LCB design for robust values, derived new dual forms, and introduces concentrability coefficients.
result Proves polynomial sample efficiency for finding ε-optimal robust policies.
Paper provides exponential convergence guarantees for Iterative Markovian Fitting.
problem Addressing the Schrödinger Bridge problem in computational optimal transport and generative modeling.
method Develops non-asymptotic exponential convergence guarantees for Iterative Markovian Fitting.
result First non-asymptotic exponential convergence guarantees for IMF under mild structural assumptions.
We give a complete characterization of the sampling complexity of best Markovian arm identification in one-parameter Markovian bandit models. We derive instance specific nonasymptotic and asymptotic lower bounds which generalize those of the IID setting. We analyze the Track-and-Stop strategy, initially proposed for th…
Unified approach for first-order methods with Markovian noise in stochastic optimization and variational inequalities.
problem Stochastic optimization problems with Markovian noise.
method Unified theoretical analysis of first-order gradient methods using randomized batching and multilevel Monte Carlo.
result Optimal (linear) dependence on the mixing time of the noise sequence, eliminating previous limiting assumptions.
We show that when the price process S represents a fully incomplete market, the optimal super-replication of any Markovian claim g(ST) with g(⋅) being nonnegative and lower semicontinuous is of buy-and-hold type. Since both (unbounded) stochastic volatility models and rough volatility models are examples of …