Study state-dependent Hawkes processes for limit order book modeling.
problem Modeling feedback loop between order flow and limit order book shape.
method Existence and uniqueness of state-dependent Hawkes processes, simulation, maximum likelihood estimation.
result Excitation effects in order flow are strongly state-dependent.
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.
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.
Detects anomalies in multiple processes using hidden Markov models.
problem Detecting an anomalous process among many with hidden states.
method Sequential search strategy using ADHM algorithm.
result ADHM algorithm effectively leverages temporal correlations.
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.
A new method uses active learning to monitor industrial processes more accurately.
problem Classifying process states (IC, OC) with limited labeled data.
method Stream-based active learning for partially hidden Markov models.
result Improved dynamic recognition of process states, especially unseen classes.
Spectral methods reduce the complexity of Markov processes.
problem Modeling and simplifying state-transition systems.
method Spectral decomposition and state aggregation.
result Developed methods to estimate low-rank Markov models.
The paper develops a state-space approach to deep Gaussian processes for efficient state estimation.
problem Efficient regression and state estimation for deep Gaussian processes.
method Hierarchical transformed Gaussian process priors, state-space representation, linear stochastic differential equations, sequential methods.
result The state-space approach enables efficient state estimation and regression for deep Gaussian processes.
Paper connects state-space models to Gaussian Processes for time series.
problem Time series modeling and forecasting with state-space models.
method Transformed state-space models into Gaussian Process kernels.
result Correct and appropriate GP kernels for Gaussian Process Regression.
New model for insurance states using Markov jump processes with non-countable state space.
problem Modeling insurance states with non-countable state spaces.
method Developed a new Thiele's differential equation for continuous time rehabilitation rates.
result Allows for consistent calculation of reserves in disability insurance.
Online learning improves state estimation of nonlinear systems.
problem Online learning of nonlinear state dynamics in Gaussian state space models.
method Stochastic variational sparse Gaussian process embedded in a particle filter framework, with model updating using stochastic gradient descent.
result State estimation performance significantly improves with online learning of state dynamics.
Clarifies when certain stochastic PDEs have affine state processes.
problem Characterizing stochastic PDEs with affine state processes.
method Characterization of initial points for affine realizations.
result Characterizes the set of initial points for affine realizations.
Paper presents a robust Kalman filter for state estimation.
problem Robust state estimation under process and measurement noise.
method Generalized Bayesian approach to a Weighted Observation Likelihood Filter (WoLF) framework.
result Achieved robust state estimation against both process and measurement noise.
VSE estimates complex processes from noisy measurements without a model.
problem Estimating states of complex, model-free processes from noisy data.
method Variational state estimation using recurrent neural networks (RNNs) in both learning and inference phases.
result VSE provides a competitive state estimate for a benchmark process (Lorenz system) compared to known and data-driven methods.
Improves event prediction in complex processes using Petri nets and deep learning.
problem Predicting the next event in complex processes given a state.
method Enhanced Petri net model with time decay functions and deep learning.
result Significant performance improvements over state-of-the-art methods.
A Hawkes process with state-dependent factor models order flows in limit order books.
problem Modeling order flows in limit order books for better market prediction.
method A Hawkes process with a state-dependent factor for conditional intensity estimation.
result State-dependent formulations improve the fit of LOB models to financial data.
New method for QPT without needing to know or prepare specific input states.
problem Quantum process characterization with unknown input states.
method Blind Quantum Process Tomography (BQPT) with single-preparation methods.
result Ability to characterize quantum processes using arbitrary unknown input states.
Machine learning aids excited-state molecular dynamics studies.
problem Challenges in studying electronically excited states of molecules.
method Employing machine learning techniques for excited-state molecular dynamics.
result Highlight successes and challenges in machine learning for excited-state processes.
Efficiently learns Gaussian process state space models using particle MCMC.
problem Flexible specification of prior assumptions for unknown dynamics.
method Projection onto approximate eigenfunctions and particle MCMC algorithm.
result Competitive performance and reliable uncertainty quantification.
Model credit ratings using economic states with Markov chains.
problem Credit rating migration influenced by economic state changes.
method Developed a Markov chain model for credit ratings conditional on economic states.
result Derived asymptotic behavior of the rating process using Markov theory.
This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this model the particle follows a simple multi-step process in velocity space which a…
The paper analyzes multivariate payments in multi-state life insurance using Markovian state processes.
problem Analyzing joint effects of life annuities and death benefits in a multi-state framework.
method Introduces multivariate present value of future payments, derives differential equations and moment generating functions, and focuses on pair-wise covariances.
result Derives Hattendorff type results for pair-wise covariances in a disability model.
Improves Gaussian process models for large datasets.
problem Complexity and memory limitations in Gaussian process models.
method Combines variational sparse approximation and state-space formulation.
result Significant computational and memory savings for large datasets.
Active learning selects inputs for GPSSM to learn latent states.
problem Optimally learn latent states of a GPSSM through active selection of inputs.
method Use mutual information to select informative inputs; approximate mutual information for GPSSM.
result Effective active learning of GPSSM dynamics in physical systems.
Solves optimal control for stochastic processes with absorbing states.
problem Optimal control of stochastic processes with absorbing states.
method Solves through system of partial differential equations.
result Explicit solution for Merton portfolio problem with default probability.
A novel multi-resolution Gaussian process model for efficient time traversal.
problem Inference for long sequences with fast and slow transitions is difficult.
method A novel Gaussian process state-space architecture composed of multiple components, each trained on a different resolution.
result The combined model allows efficient inference for arbitrarily long sequences with complex dynamics.
New algorithm for Bayesian inference in population Markov Jump processes.
problem Challenges in Bayesian inference for continuous time, discrete state systems with infinite state-space.
method Pseudo-marginal sampling algorithms based on random truncation method.
result Significant savings in computational time compared to state-of-the-art methods.
We explicitly test if the reliability of credit ratings depends on the total number of admissible states. We analyse open access credit rating data and show that the effect of the number of states in the dynamical properties of ratings change with time, thus giving supportive evidence that the ideal number of admissibl…
GPPSTD uses Gaussian Processes for efficient RL in continuous states.
problem Efficient reinforcement learning in continuous state spaces.
method Gaussian Process Posterior Sampling Reinforcement Learning (GPPSTD) algorithm.
result Combining demonstration and exploration improves reinforcement learning efficiency.
A new asset allocation model uses Markov states from clustered efficient frontier coefficients.
problem Characterizing market regimes using efficient frontiers for better asset allocation.
method Hierarchical clustering of monthly efficient frontier coefficients to define states, then a Markov process on these states for portfolio optimization.
result The model significantly outperforms benchmark portfolios empirically.
New algorithms learn MDPs with continuous states and actions using Gaussian processes.
problem Online learning in unknown, episodic MDPs with continuous states and actions.
method Developed variants of UCRL and posterior sampling algorithms using Gaussian process priors.
result Sublinear regret bounds for learning MDPs with specific kernel structures.
ETGPSSM efficiently models high-dimensional, non-stationary systems with reduced complexity.
problem Prohibitive computational and parametric complexity in high-dimensional, non-stationary dynamical systems.
method ETGPSSM integrates a single shared GP with input-dependent normalizing flows for scalable and flexible modeling.
result ETGPSSM outperforms existing models in computational efficiency and accuracy.
First we provide a simple set of sufficient conditions for the weak convergence of scaled affine processes with state space R+×Rd. We specialize our result to one-dimensional continuous state branching processes with immigration. As an application, we study the asymptotic behavior of least squares estimators…
We solve a broad class of sequential decision-making problems with partially observed states.
problem Sequential decision-making under uncertainty with partially observed states.
method Modeling as a partially observed Markov decision process (POMDP) and separating state and modulation process.
result The approach allows for specialized approximate solution procedures.
Study Markov cubature rules for polynomial processes.
problem Tractability of path-dependent tasks in polynomial process models.
method Discretizations using finite state Markov processes with moment matching conditions.
result Markov cubature rules aid American option pricing.
The method infers Markov process parameters from steady state snapshots.
problem Inferring parameters from non-equilibrium steady states without Boltzmann distribution.
method Propagator likelihood based on fictitious transitions.
result Efficient reconstruction of parameters in various systems.
Polynomial processes model energy prices with rich dynamics.
problem Modeling extreme energy price behavior.
method Developed one- and two-factor models using polynomial processes.
result Polynomial processes generate rich dynamics suitable for extreme price behavior.
Paper estimates risks in MDPs using state lumping and SAT, showing its effectiveness.
problem Estimating risks in Markov decision processes with state augmentation.
method State augmentation transformation, isotopic states, and state lumping.
result SAT and state lumping effectively estimate mean-variance and exponential utility risks.
A novel method uses GPLFMs for joint input-state estimation in linear structural systems.
problem Combined state and input estimation of linear structural systems.
method Gaussian process latent force models (GPLFMs) combined with Kalman filters.
result GPLFMs outperform conventional Kalman filters in state and input estimation.
Flexible nonlinear Hawkes processes for time-varying systems.
problem Limited expressive ability of classic Hawkes processes.
method Flexible state-switching Hawkes processes with latent variable augmentation for Bayesian inference.
result Superior performance compared to state-of-the-art competitors.
State-space systems generate probabilistic dependencies between inputs and outputs.
problem Understanding probabilistic dependencies in state-space systems.
method Introducing a probabilistic framework and proving sufficient conditions for output existence and uniqueness.
result State-space systems can generate probabilistic dependencies, even without functional relations.
Recurrent Neural Processes model time series with conditional independence to capture slow variabilities efficiently.
problem Modeling time series data with slow long-term variabilities efficiently.
method Recurrent Neural Processes (RNP) model state space with conditional independence among subsequences.
result RNP state spaces improve predictive performance on real-world time-series data and nonlinear system identification.
Flexible model learns nonlinear systems using basis functions and Gaussian process priors.
problem Learning nonlinear dynamical systems with flexibility and generalization.
method State-space model with basis function expansions and Gaussian process priors. Efficient learning via sequential Monte Carlo.
result Promising results on benchmarks and real data, indicating model's effectiveness.
Develops EM algorithm for analyzing multi-curve data with switching nonparametric regression models.
problem Analyzing multi-curve data with switching latent state processes.
method Switching nonparametric regression models and an EM algorithm for parameter estimation.
result Frequentist properties of parameter estimates validated through simulation studies and real data application.
We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the definition of an affine process, namely as stochastically continuous time-homogeneous Markov process with exponential affine Fourier-…
Generative models learn latent process to match target distributions.
problem Training flow-matching models with auxiliary stochastic dynamics.
method Introduces latent process generator matching, treating generative state as a deterministic image of a Markov process.
result Learn generator of a stochastic process with same marginal distributions.
Enhances HDP-HMM for state transitions between similar states.
problem Improving state transition probabilities between related states.
method Defines a similarity function and scales transition probabilities by it, using a Markov Jump Process with conditional conjugacy.
result Achieves favorable comparisons to existing models on various tasks.
Feature selection predicts immune state changes in RA mouse model.
problem Predicting the immune state change after RA immunotherapy.
method Feature selection algorithms applied to mouse CIA model data.
result Selected features predict both T cell markers and treatment efficacy.