New SDEs use G-Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced G-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 G-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.
Improved sampling from mean-field stationary distributions.
problem Sampling from the stationary distribution of mean-field SDEs.
method Decoupling the problem into two aspects: approximation of mean-field SDE and sampling from finite-particle distribution.
result Improved guarantees in various settings, including optimizing neural networks.
We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process X(t) and a \emph{predictive mean-field} backward SDE (BSDE) in the unknowns Y(t),Z(t),K(t,⋅). The driver of …
Study improves L∞ estimates and extreme value behavior in stochastic differential games.
problem Analyzing the mean-field limit of diffusive games through master equation.
method Using the Master Equation to approximate state processes and establishing L∞ estimates for the total error. result Established No∞ asymptotic behavior of upper order statistics of Nash states, initiating Extreme Value Theory for stochastic differential games. The paper solves complex control problems using neural networks.
problem Solving McKean-Vlasov control problems.
method Mean-field neural networks and algorithms based on dynamic programming and stochastic maximum principle.
result Extensive numerical results show the accuracy of the proposed algorithms.
Study on LOB dynamics using mean-field game theory.
problem Modeling liquidity dynamics in limit order books.
method Mean-field stochastic differential equation and control problem formulation.
result Equilibrium density function of LOB can be derived.
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance function…
We analyze linear McKean-Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-weighted spaces as well as a {convergence} result of the solution…
New framework for analyzing games with multi-dimensional singular controls and non-linear jumps.
problem Analyzing games with multi-dimensional singular controls and non-linear jump impacts.
method Probabilistic framework with novel class of MFGs (MFGs of parametrisations).
result Existence of equilibria and equivalence with MFGs of singular controls.
New MFG model for MV portfolio management with peer-based risk aversion.
problem Time-inconsistent mean-variance portfolio management with peer-based risk aversion.
method Mean-field game, smooth regularization, fixed-point arguments, convergence analysis.
result Existence of mean-field equilibrium in time-inconsistent MFG.
Noise can stabilize systemic risk models with uncertain robustness.
problem Understanding systemic risk in financial systems with uncertain parameters.
method Analyzing a mean-field model of systemic risk with uncertain coefficients and noise.
result Noise can induce stability in systemic risk models, contrary to intuition.
Deep learning solves complex PA mean field games with market-clearing conditions.
problem Optimizing Principal-Agent interactions in renewable energy markets with market-clearing conditions.
method Actor-critic approach, deep backward stochastic differential equations (BSDE), neural net approximation.
result Efficacy of the deep learning algorithm in solving complex PA mean field games.
Study uses MFG approach to model equilibrium pricing with market clearing condition.
problem Continuous asset pricing with market clearing condition.
method Mean field game approach to solve forward-backward SDEs of McKean-Vlasov type.
result Net order flow converges to zero in large N-limit with specified conditions.
New algorithm infers trajectories from partial observations using optimal transport.
problem Inferring trajectories from partial observations of coupled systems.
method Extends MFL algorithm to latent SDEs using observable state space models and partial observations.
result Experiments show significant outperformance over latent-free baseline.
DeepGSB solves MFGs with non-differentiable preferences.
problem Solving MFGs with non-differentiable preferences and exact population convergence.
method Generalized Schrödinger Bridge via Forward-Backward SDEs and Temporal Difference learning.
result DeepGSB provides necessary and sufficient conditions for mean-field problems.
Study mutual insurance market dynamics using mean field games.
problem Understanding strategic interactions and wealth distribution in mutual insurance companies.
method Extended mean field game framework, mean field forward-backward stochastic differential equations (MF-FBSDE), deep BSDE algorithm.
result Established global-in-time existence and uniqueness of Nash equilibrium strategy.
New dynamics for SGD in small learning rate regime.
problem Improving stochastic gradient descent in small learning rate regime.
method Introducing stochastic modified flows and distribution dependent stochastic modified flows.
result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.
Study shows rate of convergence for particle approximation of PDEs in Wasserstein space.
problem Analyzing convergence rates for particle approximations of PDEs in Wasserstein space.
method Backward stochastic differential equations techniques.
result Proved a rate of convergence of order 1/N for pathwise error and 1/sqrt(N) for L2-error on the derivative.
Parameter inference for stochastic differential equations is challenging due to the presence of a latent diffusion process. Working with an Euler-Maruyama discretisation for the diffusion, we use variational inference to jointly learn the parameters and the diffusion paths. We use a standard mean-field variational appr…
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 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 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 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.
Framework detects tipping points in complex systems using ML.
problem Detecting tipping points in complex, emergent systems.
method Combining manifold learning, neural networks, and Gaussian processes.
result Reduced-order models for mesoscopic and mean-field dynamics.
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.