Estimates drift functions in SDEs using denoising diffusion models.
problem Estimating time-homogeneous drift functions in multivariate SDEs.
method Formulates drift estimation as a denoising problem, trains a conditional diffusion model.
result Proposed estimator matches classical methods in low dimensions and remains competitive in higher dimensions.
New risk bound for drift estimator in stochastic models.
problem Theoretical guarantees for drift estimation in stochastic differential equations.
method Derives an explicit risk bound using diffusion model theory.
result Explicit decomposition of risk into multiple sources of error.
New method identifies SDE drift and diffusion from temporal data.
problem Learning SDE parameters from temporal data, especially in noisy or incomplete data.
method Entropy-regularized optimal transport, APPEX algorithm.
result Can almost always recover drift and diffusion from temporal marginals.
This paper extends neural network approximation results to denoising diffusion models.
problem Improving the efficiency and accuracy of generative models.
method Leveraging connections to stochastic control and neural network approximation.
result Established neural network approximation results for the Föllmer drift are extended to denoising diffusion models.
Study builds a classifier for diffusions with unknown diffusion but known drifts.
problem Multiclass classification of S.D.E. paths with unknown diffusion coefficient.
method Plug-in classifier using nonparametric estimators of drift and diffusion functions.
result Consistent classification procedure with rate of convergence under different assumptions.
This paper identifies drift Lipschitz budget K as key to diffusion policy expressivity and statistical trade-offs.
problem Understanding and maximizing the expressivity of diffusion policies while managing statistical limitations.
method Identifying drift Lipschitz budget K as central, quantifying expressivity and statistical behavior, proving lower bounds, and providing practical implementation guidelines.
result Balancing expressivity and statistical complexity yields a finite-sample performance gap, with rates depending on sample size and drift type.
New method identifies drift and diffusivity from SDE marginals.
problem Challenging task to identify drift and diffusion from SDE population dynamics.
method Proposes nn-APPEX, a Schrodinger Bridge-based inference method.
result Gradient-flow drift and Brownian diffusivity jointly identifiable from marginals.
The paper develops a neural network-based classifier for diffusion process drifts.
problem Classifying diffusion processes with distinct drift functions from discrete observations.
method Derives a Bayes rule and constructs a plug-in classifier using neural networks to estimate drifts.
result Establishes convergence rates for misclassification risk, highlighting benefits of diffusion structure.
The paper compares PINN methods for solving drift-diffusion equations on metric graphs.
problem Solving drift-diffusion equations on metric graphs using machine learning.
method Comparison of physics-informed neural networks (PINNs) for solving drift-diffusion equations on metric graphs.
result PINNs offer a flexible and versatile tool for solving parameter identification or optimization problems on metric graphs.
DPS uses PINNs to estimate drift in diffusion models for sampling.
problem Accurately estimating drift term in reverse SDE from unnormalized density.
method Diffusion-PINN Sampler (DPS) solves PINN for log-density of SDE marginals.
result DPS achieves convergence guarantees and accurately samples complex distributions.
DriftLite improves inference quality of diffusion models without retraining.
problem Adapting pre-trained diffusion models to new target distributions without retraining.
method Lightweight, training-free particle-based approach that steers inference dynamics with optimal stability control.
result Consistently reduces variance and improves sample quality over existing methods.
The paper develops a neural network method for estimating drift functions of diffusion processes from discrete observations.
problem Nonparametric estimation of drift function for diffusion processes from high-frequency discrete observations.
method Neural network-based estimator for drift function estimation.
result Derives a non-asymptotic convergence rate for the neural network estimator.
New research shows some distributions hard to sample via diffusions.
problem Some distributions hard to sample via diffusions.
method Learning drifts of diffusions to approximate target distributions.
result Superpolynomially close drifts can yield very far approximations.
We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to model two-alternative forced choice decisions, and, while simple formulae for ac…
The paper tackles singularities in diffusion models on submanifolds.
problem Analyzing singularities in diffusion models on lower-dimensional submanifolds.
method Small-time approximations of the Green's function and derivation of a new target function.
result The new target function remains bounded for singular data distributions.
The paper analyzes how synthetic data training degrades diffusion models, providing bounds and characterizing different drift regimes.
problem The degradation of performance in diffusion models trained on synthetic data.
method Theoretical analysis of score-based diffusion models, focusing on the accumulated divergence between generated and target distributions.
result Upper and lower bounds on the accumulated divergence, providing the first lower bound for diffusion models.
Geodesic walks converge to Brownian motion on Finsler manifolds.
problem Understanding random walks on Finsler manifolds.
method Analyzing convergence of geodesic random walks to diffusion processes.
result The Brownian motion on a Riemannian metric is a key result.
Graphs approximate semigroups for diffusion on Riemannian manifolds.
problem Approximating semigroups for diffusion on Riemannian manifolds.
method Discretized approximation using random walks on proximity graphs.
result Quantitative error estimates for convergence of discrete semigroups to continuous semigroups.
Efficiently reconstructs jump-diffusion processes from data using neural networks.
problem Reconstructing jump-diffusion processes from data.
method Temporally decoupled squared Wasserstein distance method using parameterized neural networks.
result Enhanced reconstruction of jump-diffusion processes from data.
We solve continuous-time latent SDE identifiability using diffusion shifts.
problem Identifiability of latent SDEs in continuous-time time series.
method Environment-induced shifts in diffusion covariance for additive-noise latent SDEs.
result Two diagonal diffusion regimes with distinct variance ratios identify latent coordinates up to permutation and scaling.
It is generally understood that a given one-dimensional diffusion may be transformed by Cameron-Martin-Girsanov measure change into another one-dimensional diffusion with the same volatility but a different drift. But to achieve this we have to know that the change-of-measure local martingale that we write down is a tr…
This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially-observed problem is reformulated into one with full observations, via a change of probability measure which removes the drift. The optimal impulse controls can be ex…
This paper investigates a financial market where returns depend on an unobservable Gaussian drift process. While the observation of returns yields information about the underlying drift, we also incorporate discrete-time expert opinions as an external source of information. For estimating the hidden drift it is crucial…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics Letters A (346), 2005] and put the application of the method on a firm theoretical …
Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance sense the contingent claim in incomplete financial market with arbitrary informatio…
LightSBB-M improves generative diffusion modeling with lower 2-Wasserstein distances.
problem Improving generative diffusion models using Schrödinger Bridge and Bass methods.
method Optimizes SBB transport plan with dual representation and tunable beta parameter.
result Achieves up to 32% improvement in 2-Wasserstein distance on synthetic datasets.
In this paper, we study term structure movements in the spirit of Heath, Jarrow, and Morton [Econometrica 60(1), 77-105] under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian motion. The G-Brownian motion represents the uncertainty about the volatility. With…
Method learns SDEs from data snapshots.
problem Learning drift and diffusion of SDEs from data.
method Two-step process: learn drift by expected value, learn diffusion by SDP.
result Validated on examples and simulations.
This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts around a constant level, with a speed of mean reversion that is affine in the in…
We present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual application of the so-called diffusion canonical transformation method that combines smoo…
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the …
Generative model for hypergraphs captures complex interactions without pairwise reductions.
problem Challenges in generating realistic hypergraphs with pairwise reductions.
method Structured stochastic diffusion on relaxed incidence matrices.
result Generative model preserves structure-aware noising and yields explicit Gaussian law.
Kernel-Gradient Drifting improves generative modeling for non-Euclidean data.
problem Challenges in generative modeling for non-Euclidean data.
method Replaces Euclidean displacement with kernel-induced directions, exposing score-based structure.
result Kernel-gradient drifting enables state-of-the-art one-step generation for non-Euclidean data.
Improved generative models for rare events using nonlinear diffusion.
problem Challenges in modeling rare conditional distributions with linear diffusion models.
method Adapting data representation and forward scheme for nonlinear drift term.
result Significant improvement in capturing extreme tail events.
Algorithm minimizes risk for multiclass classification of stochastic diffusion paths.
problem Multiclass classification of stochastic diffusion paths with distinct drift functions.
method Empirical risk minimization using L2 risk.
result Achieves fast rates of convergence under margin assumption.
Develops a new model for pricing without arbitrage opportunities.
problem Arbitrage opportunities in standard jump-diffusion models.
method Introduces a multi-type jump-diffusion model with diffusion-dependent jumps.
result Derives no-arbitrage condition linking drift to model parameters.
Estimates neural drift for stochastic equations, improving inference on noisy data.
problem Estimating drift in stochastic differential equations with neural networks.
method Non-parametric estimation using ReLU neural networks, enforcing theoretical bounds.
result Practical method for inference on noisy and rough functional data.
Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.
problem Calibrating local volatility models with stochastic drift and diffusion.
method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.
result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.
Neural Diffusion Intensity Models simplify Cox processes inference.
problem Intractable nonparametric estimation and posterior inference of latent stochastic intensity in Cox processes.
method Variational framework using neural SDEs, with theoretical guarantee of ELBO maximization coinciding with maximum likelihood estimation.
result Accurate recovery of latent intensity dynamics and posterior paths with significant speedup.
The paper predicts cryptocurrency prices using a path-dependent Monte Carlo simulation.
problem Forecasting cryptocurrency prices with volatility and jumps.
method Merton's jump diffusion model with machine learning, traditional, and statistical methods.
result Introduced a path-dependent Monte Carlo simulation for cryptocurrency price prediction.
The paper optimizes interpolation schedules in generative models to improve sampling accuracy.
problem Improving sampling accuracy in generative models with fewer resources.
method Minimizing the averaged squared Lipschitzness of the drift field, using transfer formulas.
result Designed schedules yield more accurate fine-scale statistics at fixed integrator budget.
ML-EM method speeds up diffusion model sampling.
problem Efficiently sampling from complex diffusion models.
method Multilevel Euler-Maruyama method with UNet approximations.
result Polynomial speedup in sampling from diffusion models.
Unified kernel for prediction markets reduces belief variance forecast error.
problem Lack of standardized tools for quoting and hedging belief risk in prediction markets.
method Logit jump-diffusion model with risk-neutral drift, calibration pipeline, and coherent derivative layer.
result Model reduces forecast error compared to diffusion-only and probability-space baselines.
We discuss utility based pricing and hedging of jump diffusion processes with emphasis on the practical applicability of the framework. We point out two difficulties that seem to limit this applicability, namely drift dependence and essential risk aversion independence. We suggest to solve these by a re-interpretation …
Unified framework for generating synthetic financial time series that accurately capture both marginal distributions and temporal dynamics.
problem Generating synthetic financial time series that reproduce both marginal distributions and temporal dynamics.
method SBBTS: A unified Schrödinger-Bass framework for synthetic financial time series.
result SBBTS accurately recovers stochastic volatility and correlation parameters that prior methods fail to capture.
Method recovers causal diffusion mechanisms from steady-state data without parametric assumptions.
problem Recovering causal diffusion mechanisms from steady-state gene expression data.
method Non-parametric kernel estimator for drift function, cross-validation for hyperparameter tuning.
result Full causal mechanism can be non-parametrically identified under weak non-explosion criterion.
Adaptive sampling improves graph diffusion models by maintaining uniform information speed.
problem Standard diffusion models overlook non-homogeneous dynamics on complex manifolds.
method Information-geometric framework using Fisher-Rao metric and Drift Variation Score (DVS).
result DVS solver ensures uniform rate of distributional change, improving structural fidelity and efficiency.
We consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We describe the possible small time heat kernel expansion on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the dri…