In the paper [Probab. Theory Relat. Fields, 100 (1994) 417-428] Xue-Mei Li has shown that the moment stability of an SDE is closely connected with the topology of the underlying manifold. In particular, she gave sufficient condition on SDE on a manifold under which the fundamental group . We prove that in …
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.
168,695 papers · 148 categories
Trend · papers per month
48 results for “contractive SDEs”
Neural networks improve financial derivative pricing accuracy.
problem Improving accuracy in financial derivative pricing.
method Use neural networks to model drift and volatility in SDE models, optimize using SGD for European options and PDE for American options.
result Neural network models outperform traditional models in pricing derivatives.
A new sampling method called Restart improves both speed and quality of generative processes.
problem Balancing speed and quality in generative processes involving differential equations.
method Alternates between adding noise and following ODE, improving both speed and quality.
result Surpasses previous SDE and ODE samplers in both speed and accuracy.
Paper proposes new Langevin samplers for sampling from log-concave distributions with superlinear gradient growth.
problem Sampling from log-concave distributions with superlinear gradient growth.
method Proposes two novel discretizations of kinetic Langevin SDEs, showing contractivity and log-Sobolev inequality.
result Establishes non-asymptotic bounds in 2-Wasserstein distance between sampled distributions and target measures.
LMC achieves sqrt(d) dependence in sampling error, improving previous bounds.
problem Analyzing sampling error in Langevin Monte Carlo.
method Refined mean-square analysis for discretizations of contractive SDEs.
result Establishes mixing time bound for LMC.
The paper tackles robust control for insurance contracts under uncertain transition rates.
problem Maximizing utility in insurance contracts with uncertain transition rates.
method Novel robust utility maximization problem under bounded cumulative transition rate uncertainty, using worst-case scenario analysis.
result Existence and uniqueness of worst-case and best-case reserves for insurance contracts.
Pricing equity-linked life insurance contracts with multiple risk factors by neural networksq-fin.PR
The paper uses neural networks to price complex life insurance contracts with multiple risk factors.
problem Pricing equity-linked life insurance contracts with various stochastic risk factors.
method Assuming hedging to reduce local variance, the price is expressed as a system of non-linear PDEs. Reformulated as a backward SDE with jumps, solved numerically using neural networks.
result Neural networks provide an efficient numerical solution for pricing these complex contracts.
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
In this work we study the price-hedge issue for general defaultable contracts characterized by the presence of a contingent CSA of switching type. This is a contingent risk mitigation mechanism that allow the counterparties of a defaultable contract to switch from zero to full/perfect collateralization and switch back …
Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexitymath.PR
We present an improved analysis of the Euler-Maruyama discretization of the Langevin diffusion. Our analysis does not require global contractivity, and yields polynomial dependence on the time horizon. Compared to existing approaches, we make an additional smoothness assumption, and improve the existing rate from $O(η)…
SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equationsstat.ML
SDE Matching eliminates simulation for training Latent SDEs, achieving similar performance.
problem Training Latent SDEs with adjoint sensitivity methods is computationally expensive and limited.
method SDE Matching, inspired by Score- and Flow Matching, eliminates simulation for training Latent SDEs.
result SDE Matching achieves performance comparable to adjoint sensitivity methods while reducing computational complexity.
New SDEs use -Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced -SDEs with coefficients dependent on current state and solution as random variable.
result Validated new SDE framework for complex stochastic systems.
Study on the smoothness of solutions to a specific type of stochastic differential equation.
problem Regularity of solutions to mean-field -SDEs.
method Analysis of first and second order Fréchet differentiability in the random initial condition.
result Established the Fréchet differentiability of the solution and specified the corresponding equations.
New SDE model for continuous-time reinforcement learning.
problem Modeling exploration in continuous-time reinforcement learning.
method Introduced grid-sampling SDE as a proxy model.
result Wellposedness of the SDE in the presence of jumps.
This paper uses SDEs to analyze GANs training and long-run behavior.
problem Understanding the training process and long-run behavior of GANs.
method Established SDE approximations for GANs training and analyzed long-run behavior via invariant measures.
result The long-run behavior of GANs training can be studied via the invariant measures of its SDE approximations.
The paper identifies generators of linear SDEs with noise types.
problem Identifying the generator of linear SDEs from their solution distribution.
method Deriving sufficient and necessary conditions for additive noise, and sufficient conditions for multiplicative noise.
result Generic conditions for identifying the generator of linear SDEs with both types of noise.
Simulation-free VI closes the approximation gap in latent SDEs
problem Recovering dynamical systems from noisy observations
method Helmholtz-SDE
result Recovers dynamics more faithfully than prior methods
Sig-SDE model integrates signatures with SDEs for financial data.
problem Calibrating models to exotic financial products with non-linear dependencies.
method Integrating signatures from stochastic analysis with neural SDEs.
result Sig-SDE provides theoretical guarantees for convergence.
Proposes methods to include distributional information in MV-SDEs for better modeling of interacting particle systems.
problem Modeling the behavior of an infinite number of interacting particles with distributional information.
method Semi-parametric methods and estimators for MV-SDEs.
result Explicitly including distributional dependence improves performance in modeling temporal data with interaction.
New method learns SDEs without integrators, speeding up computation.
problem Computational expense in learning SDEs using neural networks.
method Importance-sampling estimator for SDEs, leveraging parallelism.
result Lower-variance gradient estimates and massive computation time reductions.
Stochastic Normalizing Flowsstat.ML
Stochastic normalizing flows use SDEs for efficient training and sampling.
problem Efficient maximum likelihood estimation and variational inference.
method Continuous normalizing flows extended with stochastic differential equations (SDEs) and rough path theory.
result Stochastic normalizing flows enable efficient training and sampling from complex distributions.
We explain how Itô Stochastic Differential Equations (SDEs) on manifolds may be defined using 2-jets of smooth functions. We show how this relationship can be interpreted in terms of a convergent numerical scheme. We show how jets can be used to derive graphical representations of Itô SDEs. We show how jets can be used…
New method speeds up SDE inference by matching moments to FPK equation.
problem Efficiency of sampling schemes in high-dimensional SDEs.
method Direct approximation of Fokker-Planck-Kolmogorov equation by matching moments.
result Fast, scalable inference in high-dimensional latent spaces.
Proposes neural SDEs with change points for better time series modeling.
problem Restrictions in modeling time series with distributional shift.
method Generative adversarial networks (GANs) for SDEs and change point detection.
result Jointly learns change points and SDE model parameters.
New geometric SDEs and discretizations on Riemannian manifolds with error bounds.
problem Modeling diffusion processes on Riemannian manifolds with geometric SDEs.
method Introduced a new construction of geometric SDEs and provided non-asymptotic error bounds.
result First non-asymptotic error bound for geometric Euler-Murayama discretization.
This paper bridges the gap between ODE and SDE in diffusion models using Fokker-Planck equations.
problem Empirical evidence shows that ODE-based samples from score-based diffusion models are inferior to SDE-based samples.
method The paper rigorously describes dynamics and approximations in training score-based diffusion models, linking them to Fokker-Planck equations.
result Adding a regularisation term based on the Fokker-Planck residual can close the gap between ODE- and SDE-induced distributions.
New method speeds up generative modeling without requiring diffusion steps.
problem Improving the speed and efficiency of generative modeling techniques.
method Probability flow ODE with a corrector step, achieving better dimension dependence.
result Better dimension dependence ( vs. , assuming smoothness of the data distribution).
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.
New algorithm optimizes nonlinear SDEs online with convergence guarantees.
problem Optimizing nonlinear stochastic differential equations (SDEs) is computationally challenging.
method Forward propagation algorithm that solves an SDE derived using forward differentiation.
result Convergence theorem for nonlinear dissipative SDEs with bounds on stochastic fluctuations.
We developed efficient methods to compute gradients for Neural SDEs, improving training speed and accuracy.
problem Training Neural SDEs requires accurate and efficient computation of gradients, which is challenging due to the complexity of SDEs.
method We introduced a reversible Heun method for solving backwards-in-time SDEs and a Brownian Interval for sampling and reconstructing Brownian motion.
result Our methods significantly improve training speed and accuracy for Neural SDEs, outperforming state-of-the-art techniques.
We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the SDEs and is strongly convergent with rate one. Moreover, we show that this general …
We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a use…
Neural SDEs reduce variance in stochastic simulations.
problem Efficiency of Monte Carlo simulations in finance.
method Use neural SDEs with control variates parameterized by neural networks.
result Prove optimality conditions for variance reduction in SDEs with infinite activity.
NSFs learn SDE transition laws for efficient sampling.
problem Efficiently sampling between arbitrary time points in SDEs.
method Conditional normalising flows with architectural constraints.
result Up to two orders of magnitude speed-ups at large time gaps.
New schemes for SDEs on manifolds keep solutions close to the manifold.
problem Solving SDEs constrained to manifolds in high accuracy.
method Geometrically invariant numerical schemes that remain close to the manifold.
result The schemes converge under standard assumptions and outperform existing methods.
Generates consistent IV surfaces using VAEs and SDE models.
problem Creating arbitrage-free IV surfaces from historical data.
method Combining VAEs with SDE models for parameter distribution, sampling, and decoding.
result Superior out-of-sample performance of the refined VAE model.
Neural SDEs model continuous sequences using neural networks.
problem Modeling continuous-time dynamics in sequence data.
method Interprets time-series as samples from a continuous dynamical system, parameterized by Neural SDE.
result Demonstrates superior performance in diverse sequence modeling tasks.
TFM trains Neural SDEs without backpropagation, improving clinical time series modeling.
problem Modeling irregularly sampled time series in medicine.
method Trajectory Flow Matching (TFM) using flow matching for generative modeling.
result TFM improves performance on clinical time series datasets.
Deep learning estimates time-varying Markov model parameters.
problem Estimating time-dependent parameters in Markov models.
method Reframes parameter estimation as an optimization problem using maximum likelihood.
result Real solution close to SDE with neural network-derived parameters under specific conditions.
Neural SDEs model suicide risk with compact state space constraints.
problem Modeling suicide risk with irregular, noisy, and partially observed data.
method Developed neural SDEs confined to compact state spaces, addressing domain constraints and numerical stability.
result Improved forecasts and optimization dynamics over standard models on EMA datasets.
SING improves state inference in latent SDE models for better drift function estimation.
problem Intractable posterior inference in latent SDE models.
method Natural gradient variational inference.
result SING provides faster and more reliable inference in latent SDE models.
Method learns latent SDEs from high-dimensional time series.
problem Learning latent stochastic differential equations from time series data.
method Self-supervised learning with variational autoencoders and Euler-Maruyama approximation.
result Can recover SDE coefficients and latent variables up to isometry with infinite data.
Improving Infinitely Deep Bayesian Neural Networks with Nesterov's Accelerated Gradient Methodstat.ML
Improved SDE-BNN model reduces NFEs and accelerates convergence.
problem High computational cost and convergence instability in SDE-BNNs.
method Nesterov's Accelerated Gradient (NAG) method integrated into SDE-BNN framework.
result Significantly reduced number of function evaluations (NFEs) and improved predictive accuracy.
Model change points in time-series data with neural SDEs and variational autoencoders.
problem Modeling change points in time-series data with neural stochastic differential equations.
method Proposes a novel model formulation and training procedure based on the variational autoencoder framework, alternating between updating neural SDE parameters and change points.
result Demonstrates the expressive power of the proposed model in modeling both classical parametric SDEs and real datasets with distribution shifts.
The paper clarifies the approximation of SGD with Ito SDEs for finite learning rates.
problem Theoretical justification and experimental verification of the Ito SDE approximation for finite learning rates in SGD.
method An efficient simulation algorithm SVAG and a necessary condition test for the SDE approximation.
result The Ito SDE approximation can meaningfully capture training and generalization properties of deep nets with finite learning rates.
Proposes a method to estimate SDE noise from a single trajectory.
problem Estimating SDE noise from a single data trajectory without ergodicity or stationarity.
method Combining Taylor expansions, Girsanov transformations, and drift function's initial value for drift and noise estimation.
result First SSISDE algorithm capable of identifying SDE dynamics from a single trajectory.
The paper develops methods to price and hedge options in path-dependent stock models.
problem Pricing and hedging options under complex stock models.
method Develops a path-dependent PDE for option pricing and differentiability of path-dependent SDE solutions.
result Provides formulas for option Greeks and differentiability of path-dependent SDE solutions.
Novel method for SDE calibration from sparse data using neural flows.
problem Calibrating SDEs from sparse, noisy observations.
method Characterization of posterior SDE using neural networks trained to solve a PDE with multiplicative updates.
result Significant improvement in scalability and accuracy compared to classical methods.