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.
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as their stochastic logarithms. We provide a structure result for continuous quasi self…
Study of affine processes without stochastic continuity assumption.
problem Time-inhomogeneous affine processes with unpredictable jumps.
method Developed a general theory of finite dimensional affine semimartingales under weak assumptions.
result Affine form of semimartingale characteristics and solutions to Riccati equations.
CLPF models continuous time-series data with improved representational power and variational approximations.
problem Fitting continuous time-series data with existing models faces challenges in representational power and variational quality.
method CLPF uses a time-dependent normalizing flow driven by a stochastic differential equation to decode continuous latent processes into continuous observables. Maximum likelihood optimization is achieved through a novel variational posterior process.
result CLPF outperforms state-of-the-art baselines on synthetic and real-world time-series data.
This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of non-constant price processes has to be 2, as in the case of continuous martingales.
New method for fluid approximation of CTMCs without population structure.
problem Approximating the macro-scale behavior of large CTMCs.
method Spectral analysis of CTMC transition matrix, diffusion maps, Gaussian process regression.
result Construct an ODE approximating CTMC mean in continuous space.
Study the limits of discrete DPPs to continuous DPPs as set size grows.
problem Characterize the behavior of discrete DPPs as they approach continuous DPPs.
method Non-asymptotic characterization of the limit in terms of weak coherency.
result Sufficient conditions for weak coherency are identified.
A scalable framework for inference in continuous Cox processes using Gaussian processes.
problem Inference in inhomogeneous Poisson processes with continuous intensity functions.
method Structured variational approximation of likelihood through augmentation with superposition of Poisson processes.
result Structured variational approximation captures dependencies across variables and outperforms mean-field methods and sampling schemes.
Logarithmic regret for continuous-time reinforcement learning.
problem Continuous-time Markov decision processes with unknown transition probabilities and holding times.
method Upper confidence reinforcement learning, mean holding time estimation, stochastic comparison of point processes.
result Logarithmic regret bound achieved in finite time.
New method infers and samples point processes from latent diffusion.
problem Modeling point processes with latent diffusion.
method Itô's excursion theory for inference and sampling.
result Proposes a new method to infer and sample point processes.
In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e.~a least favorable frictionless market leading to the same optimal strategy and u…
New algorithm for continuous-time switching systems using variational inference.
problem Inference in time-series data with continuous-time switching systems.
method Developed a variational inference algorithm combining Gaussian process approximation and posterior inference for Markov jump processes.
result Bayesian latent state estimates and point estimates of unknown parameters for arbitrary points on the real axis.
New methods for inferring, predicting, and estimating continuous-time, discrete-event processes.
problem Inferring, predicting, and estimating entropy rate of continuous-time, discrete-event processes.
method Bayesian structural inference extended with neural networks.
result Methods are competitive for prediction and entropy-rate estimation with state-of-the-art.
Formulates superhedging under costs and uncertainty for continuous assets.
problem Superhedging with transaction costs and model uncertainty for continuous processes.
method New topological framework for continuous asset prices with parametric model uncertainty.
result Formulates a superhedging theorem in the presence of transaction costs and model uncertainty.
Bayes-CPACE optimally explores continuous BAMDPs.
problem Model uncertainty in continuous state and action spaces.
method Covering state-belief-action space with samples, exploiting Lipschitz continuity.
result Near-optimal value function computed efficiently.
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.
VAR-GPs solve continual learning by updating posteriors sequentially.
problem Catastrophic forgetting in sequential learning tasks.
method Sparse inducing point approximations and auto-regressive variational distribution.
result VAR-GPs prevent catastrophic forgetting and outperform baselines.
Study local expansions of continuous-time processes using Ito signature properties.
problem Analyzing local expansions of continuous-time processes and their moments.
method Using the Ito signature, a basis of iterated integrals, to conduct expansions of the process' characteristic function.
result Explicit coefficients and stochastic representations for asymptotics as time shrinks or diverges.
Proposes a new birth-death process for better modeling of population dynamics.
problem Models of population or opinion dynamics with spurious long-range memory.
method Introduces Bessel-like birth-death process to address the spurious long-range memory.
result Derives equations for the burst and inter-burst duration of the new process.
ARPs improve exploration and sample efficiency in continuous control tasks.
problem Limited exploration in continuous control tasks leading to low sample efficiency.
method Introduce autoregressive policies (ARPs) with temporally coherent standard normal distributions.
result ARPs enhance exploration and sample efficiency in both simulated and real-world domains.
New RL framework models continuous-time dynamics using neural ODEs.
problem Modeling continuous-time dynamics in semi-Markov decision processes.
method Model-based reinforcement learning with neural ODEs.
result High-performing policies developed with minimal data.
A new normalizing flow models continuous stochastic processes efficiently.
problem Efficient modeling of continuous stochastic processes.
method Dynamic normalizing flows driven by Wiener process.
result Rich time series model with efficient computation of likelihoods and marginals.
A new video prediction model treats videos as continuous processes, reducing sampling steps and improving efficiency.
problem Efficiency and temporal coherence in video prediction models.
method Treats videos as a continuous multi-dimensional process, reducing sampling steps.
result Reduction of 75% sampling steps, state-of-the-art performance on benchmark datasets.
Continuous time framework for discrete data denoising models.
problem Efficient training and sampling for discrete data denoising models.
method Formulated as Continuous Time Markov Chains (CTMCs), efficient training using continuous time ELBO, high-dimensional CTMC simulation, novel theoretical error bound.
result Continuous time treatment enables novel theoretical error bound between generated and true data distributions.
Paper introduces a new framework for MAB processes with arm switch restrictions.
problem Optimizing decisions among multiple options with switching constraints.
method Develops a Gittins index process for MAB with arm switch restrictions.
result Establishes optimality of Gittins index policies for the new framework.
A new RG approach connects discrete and continuous time descriptions of Gaussian processes.
problem Discretization of continuous stochastic processes for accurate simulation or model inference.
method Renormalization Group (RG) approach for Gaussian time series generated by auto-regressive models.
result RG fixed points correspond to discretizations of linear SDEs, providing insights into process accuracy.
Paper tackles risk-sensitive impulse control for continuous-time processes.
problem Risk-sensitive impulse control for continuous-time Feller-Markov processes.
method Probabilistic approach to solve Bellman equation and construct optimal strategy.
result Optimal strategy approximated by dyadic impulse strategies.
A new method for Gaussian Processes handles mixed continuous and categorical inputs.
problem Modeling cross-correlations between continuous and categorical data.
method Low-Rank Correlation (LRC) method for Gaussian Processes with flexible rank approximation.
result LRC outperforms existing methods in estimating cross-correlations and predicting response surfaces.
Study stability of trading strategy under market perturbations.
problem Dynamic stability of trading strategy under market changes.
method Established reverse conjugacy characterizations, proved continuity and convergence of indirect utility process.
result Continuity and first-order convergence of indirect utility process under market perturbations.
Working in a continuous time setting, we extend to the general case of dynamic risk measures continuous from above the characterization of time consistency in terms of ``cocycle condition'' of the minimal penalty function. We prove also the supermartingale property for general time consistent dynamic risk measures. Whe…
RL approach for continuous-time mean-variance portfolio selection with empirical validation.
problem Continuous-time mean-variance portfolio selection in unknown market coefficients.
method Reinforcement learning for diffusion processes, sublinear regret bound derivation.
result RL strategy consistently outperforms model-based counterparts, especially in volatile markets.
Generalizes PCA and ICA for continuous-time signals using neural networks.
problem Low-rank decomposition of continuous-time vector-valued signals.
method Implicit neural network framework to learn numerical approximations of PCA and ICA.
result Unified approach to PCA and ICA in continuous domain, enforcing decorrelation and independence.
Quantum computing speeds up analysis of financial stochastic processes.
problem Challenging simulation and analysis of continuous time stochastic processes.
method Established a quantum framework for efficient state preparation and information extraction.
result Extraction of path-dependent and history-sensitive information from stochastic processes efficiently.
A new method for CT-DCEGs simplifies inference for asymmetric processes.
problem Inference in asymmetric state space problems with continuous time evolution.
method An extension of CEG propagation for CT-DCEGs, employing junction tree inference.
result CT-DCEGs are preferred over DBNs and continuous time BNs for asymmetric processes.
Continuized Nesterov acceleration accelerates stochastic gradient descent and gossip algorithms.
problem Improving the convergence rate of stochastic gradient descent and gossip algorithms.
method Introducing a continuized variant of Nesterov acceleration, which mixes variables continuously and takes gradient steps at random times.
result The continuized Nesterov acceleration achieves convergence rates similar to Nesterov's original acceleration but with random parameters.
In a recent work \cite{BG}, given a collection of continuous semimartingales, authors derive a semimartingale decomposition from the corresponding ranked processes in the case that the ranked processes can meet more than two original processes at the same time. This has led to a more general decomposition of ranked pro…
A new method for continual learning using Gaussian processes.
problem Avoiding forgetting previous tasks in continual learning.
method Bayesian inference over function space, Gaussian process with inducing points.
result Strong results on benchmarks, unifying rehearsal and Bayesian perspectives.
Modeling time series with jumps using neural networks and stochastic processes.
problem Capturing the dynamics of time series with both continuous flows and discrete jumps.
method Introducing Neural Jump Stochastic Differential Equations (Neural JSDEs) that extend Neural Ordinary Differential Equations (Neural ODEs) with a stochastic process term.
result Demonstrated the model's predictive capabilities on various datasets, including Hawkes processes, Stack Overflow awards, medical records, and earthquake monitoring.
Study large deviation principle for fractional stochastic volatility models.
problem Large deviation principle for Volterra type fractional stochastic volatility models.
method Prove a small-noise large deviation principle under weaker conditions.
result Derive large deviation principle in small-time regime.
Cai, Song and Kou (2015) [Cai, N., Y. Song, S. Kou (2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3): 540-554] made a breakthrough by proposing a general framework for pricing both discretely and continuously monitored Asian options under one-dimensional Markov processes. In …
Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete setting admits an efficient sampling algorithm based on the eigendecomposition of…
IRL addresses weaknesses in DDPG and A3C for continuous reinforcement learning.
problem Theoretical weaknesses in DDPG and A3C for continuous reinforcement learning.
method IRL based on stochastic differential equations, ensuring action continuity and variance control.
result IRL method guarantees action continuity and variance control, allowing positive interaction with the environment.
Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proporti…
Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has led to some fundamentally new Monte Carlo algorithms which can be used to sample f…
Bayesian optimization tackles mixed discrete-continuous problems with Gaussian processes.
problem Optimizing problems with both discrete and continuous variables using costly simulations.
method Relaxing discrete variables into continuous latent variables, using Bayesian optimization, and incorporating compatibility constraints with Lagrangians.
result Comparative analysis of different mixed Bayesian optimization approaches.
A new method optimises problems with both continuous and categorical inputs.
problem Optimising black-box problems with mixed continuous and categorical inputs.
method Continuous and Categorical Bayesian Optimisation (CoCaBO) combining multi-armed bandits and Bayesian optimisation.
result CoCaBO outperforms existing methods on synthetic and real-world tasks.
Unified framework for inference in complex nonlinear processes.
problem Challenges in inferring nonlinear continuous stochastic processes with sparse observations and complex topologies.
method Neural Backward Filtering Forward Guiding (NBFFG) framework that constructs a variational posterior using a proxy linear-Gaussian process.
result Empirical results show NBFFG outperforms baselines on synthetic benchmarks and high-dimensional phylogenetic analysis tasks.