We determine the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a Robertson-Walker space-time. We prove in particular that when approaching the explosion time of the diffusion, its projection on the base manifold almost surely converges to a random point of the …
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48 results for “diffusive behavior”
Study on short-term behavior of ATM-IV for jump-diffusion model.
problem Analyzing the short-time behavior of ATM-IV for a specific stochastic volatility model.
method Used Malliavin Calculus techniques to derive expressions for ATM-IV level and skew.
result Short-time behavior of ATM-IV level is consistent for all pure-jump Lévy processes.
Diffusion-QL uses diffusion models to improve offline RL performance.
problem Offline RL struggles with function approximation errors on out-of-distribution actions.
method Diffusion-QL represents the policy as a conditional diffusion model and optimizes action-values.
result Diffusion-QL achieves state-of-the-art performance on D4RL benchmark tasks.
Study shows diffused interface flows to single diffused balls over time.
problem Volume-preserving mean curvature flow in Euclidean space.
method Diffused interface version, exponential convergence proof.
result Exponential convergence to single diffused balls.
Strategic traders adjust indicative prices near auctions to achieve nearly diffusive outcomes.
problem Achieving diffusive price behavior in Paris Stock Exchange auctions.
method Analyzing the diffusive properties of indicative auction prices and the strategic behavior of traders.
result Strategic traders adjust their order submission times to achieve nearly diffusive price behavior.
We present an agent behavior based microscopic model that induces jumps, spikes and high volatility phases in the price process of a traded asset. We transfer dynamics of thermally activated jumps of an unexcited/ excited two state system discussed in the context of quantum mechanics to agent socio-economic behavior an…
Study on implied volatility of an affine jump-diffusion model.
problem Characterize implied volatility of an affine jump-diffusion model.
method Explicit moment generating function derived from solving ODEs; large deviation principle applied.
result Asymptotic behaviors of implied volatility in large-maturity and large-strike regimes characterized.
Study on how non-reversible diffusion processes affect homology on manifolds.
problem Understanding the asymptotic behavior of random homology in diffusion processes.
method Investigation of asymptotic properties of random homology associated with stochastic diffusion processes on compact Riemannian manifolds.
result For quadratic rate, manifold is a locally trivial fiber bundle over a flat torus with minimal fibers.
New tools extend weak approximation of SGD algorithms to infinite time horizon.
problem Weak approximation of stochastic gradient descent algorithms in infinite time horizon.
method Backward error analysis of numerical stochastic differential equations and truncated formal power expansion.
result Characterization of asymptotic behavior of SGD algorithms for strongly convex functions.
Study naive vs sophisticated agents stopping a diffusion process with time-inconsistent payoffs.
problem Time-inconsistent stopping problem for diffusion processes.
method Analyzes naive and sophisticated agents' strategies, proving equilibrium existence.
result Equilibrium strategies can be derived as fixed points of strategic reasoning operators.
Consistency distillation reduces memorization in diffusion models without harming sample quality.
problem Understanding how distillation affects memorization in diffusion models.
method Analysis of consistency distillation in diffusion models using a random feature neural network model.
result Consistency distillation reduces memorization in diffusion models without harming sample quality.
We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson-Walker space-time. We prove in particular that the Poisson boundary of the diffusion can be identified with …
Reconstructs Riemannian geometry from diffusion properties.
problem Recovering Riemannian geometry from diffusion data.
method Intrinsic reconstruction from diffusion semigroup and calculus.
result Reveals Riemannian structure from diffusion properties.
A new method for offline RL using diffusion models and self-weighted guidance.
problem Challenges in computing scores for offline RL using weight functions.
method Constructing a diffusion over actions and weights, using the diffusion model for guidance.
result Performs on par with state-of-the-art methods on challenging environments.
We study strict local martingales via h-transforms, a method which first appeared in Delbaen-Schachermayer. We show that strict local martingales arise whenever there is a consistent family of change of measures where the two measures are not equivalent to one another. Several old and new strict local martingales are i…
Explicit moments of decision times for single- and double-threshold drift-diffusion processesq-bio.NC
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…
New method trains neural samplers to sample from multi-modal distributions efficiently.
problem Mode-seeking behavior of reverse KL divergence hinders effective sampling from multi-modal target distributions.
method Minimizing reverse diffusive KL divergence along diffusion trajectories of model and target densities.
result Demonstrated enhanced sampling performance across various multi-modal distributions.
Reaction-Diffusion-Branching Models of Stock Price Fluctuationscond-mat.stat-mech
Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent . Biase…
Simulation of Multidimensional Diffusions with Sticky Boundaries via Markov Chain Approximationmath.PR
New method simulates sticky boundaries in multidimensional diffusions.
problem Simulating sticky boundaries in multidimensional diffusions.
method Approximate sticky diffusion by a Markov chain, using either finite difference or matching local moments.
result Validates both construction methods for first-order simulation schemes.
The paper examines the sampling dynamics of diffusion models using ODEs.
problem Understanding the sampling dynamics of diffusion models.
method Careful inspection of ODE-based sampling of SDEs, revealing structures and relationships.
result Established a theoretical relationship between optimal ODE-based sampling and mean-shift algorithm.
Study explores efficient continual learning of diffusion models.
problem Efficiently reusing computation in training diffusion models as data evolves.
method Benchmarked and analyzed CL methods for Denoising Diffusion Probabilistic Models (DDPMs).
result Experience replay with reduced rehearsal coefficient shows strong performance.
Extreme Learning Machine for the Characterization of Anomalous Diffusion from Single Trajectories (AnDi-ELM)physics.data-an
ELM combines machine learning and feature engineering for anomalous diffusion detection.
problem Quantitative characterization of anomalous diffusion from single trajectories.
method Extreme Learning Machine (ELM) combined with feature engineering.
result ELM achieves satisfactory performance in AnDi challenge tasks.
Diffusion models mimic human actions in sequential tasks.
problem Cloning human behavior in dynamic environments is challenging.
method Adapting diffusion models to handle stochastic, multimodal, and correlated actions.
result Diffusion models closely replicate human behavior in robotic and gaming tasks.
Investor-driven information diffusion affects excess comovement in China and the U.S. markets.
problem Investor-driven information diffusion and its impact on excess comovement.
method Cross-sectional analysis of 4,533 Chinese and 4,517 U.S. stocks from 2010 to 2022.
result Retail-driven information diffusion significantly drives excess comovement in China, while institution-driven diffusion is the primary driver in the U.S.
DAPS++ improves diffusion-based image restoration by decoupling prior and likelihood.
problem Decoupling prior and likelihood in diffusion-based inverse problems.
method Introducing DAPS++, which fully decouples diffusion-based initialization from likelihood-driven refinement.
result Achieves high computational efficiency and robust reconstruction performance.
The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and also consider multi-factor models including stochastic volatility. Daily Eurodoll…
DAPS++ improves diffusion-based image restoration by decoupling prior and likelihood.
problem Decoupling prior and likelihood in diffusion-based inverse problems for better performance.
method Introducing DAPS++, which separates diffusion initialization from likelihood refinement.
result DAPS++ achieves high computational efficiency and robust reconstruction performance.
The paper studies expert opinions in financial markets using diffusion approximations.
problem Estimating hidden drift in financial markets with expert opinions.
method Investigates asymptotic behavior of filter for high-frequency expert opinions, derives diffusion approximations.
result Expert opinions can be approximated by a diffusion process, simplifying utility maximization problems.
Generative diffusion models gradually memorize training data, losing independent dimensions.
problem Understanding how generative diffusion models memorize training data, especially on low-dimensional manifolds.
method Measuring latent dimensionality via the learned score field, proposing a geometric memorization theory.
result Generative diffusion models experience a smooth collapse of their capacity to vary across independent directions as data become scarce, leading to near point-wise replication of salient features.
Improved diffusion bridge sampling with rKL-LD loss.
problem Improving sampling from unnormalized distributions using diffusion bridges.
method Employing the rKL-LD loss instead of the Log Variance (LV) loss for diffusion bridges.
result rKL-LD consistently outperforms LV loss in diffusion bridges.
New study on guidance in masked diffusion models, showing how it shapes sampling dynamics.
problem Understanding how guidance influences the sampling behavior of masked diffusion models.
method Derived explicit solution to guided reverse dynamics, analyzing effects in 1D and 2D.
result Guidance amplifies class-specific regions and suppresses shared regions, affecting covariance structures.
Graph Beta Diffusion (GBD) generates graphs with mixed discrete and continuous components.
problem Generating graphs with mixed discrete and continuous components.
method Introduces Graph Beta Diffusion (GBD) using a beta diffusion process.
result Competes strongly with existing models across graph benchmarks.
Weak diffusion priors can still perform well in inverse problems.
problem Using mismatched or low-fidelity diffusion priors in inverse problems.
method Extensive experiments and theoretical analysis combining Bayesian-consistency theory and local-correlation analysis.
result Weak priors succeed when measurements are highly informative, and they fail in other regimes.
Paper analyzes LPSA algorithm for constrained optimization, revealing phase transitions and bias-variance trade-offs.
problem Optimization problems with linear constraints.
method Loopless projection stochastic approximation (LPSA) with jump diffusion approximation.
result LPSA trajectories converge to SDEs, revealing asymptotic behaviors and phase transitions.
Unsupervised ML method reveals hidden features in reactive-diffusion simulations.
problem Automating interpretation of large model outputs in reactive-diffusion simulations.
method NTFk using Non-negative Tensor Factorization (NTF) coupled with k-means clustering.
result Identifies additive features characterizing mixing behavior.
CADD improves generative quality by augmenting discrete diffusion with continuous latent space.
problem Loss of semantic information between denoising steps in discrete diffusion models.
method Introduces a framework that augments discrete state space with a continuous latent space, allowing for graded, informative masked tokens.
result CADD improves generative quality across text generation, image synthesis, and code modeling.
New diffusion models capture heavy-tailed distributions better.
problem Diffusion models struggle with rare or extreme events in heavy-tailed distributions.
method Repurposed diffusion framework using multivariate Student-t distributions, tailored perturbation kernel, and -divergence.
result Our models generate rare and extreme events more effectively than standard diffusion models.
Study shows how diffusion models learn on low-dimensional manifolds.
problem Learning efficiency of diffusion models on manifolds.
method Analyzes denoising score matching with random feature neural networks.
result Sample complexity scales linearly with intrinsic dimension, not ambient dimension.
Uniform diffusion approximation for SGD in non-convex settings.
problem Finite-time diffusion approximation for SGD.
method Establishing uniform-in-time diffusion approximation with strong convexity and mild conditions.
result Uniform-in-time diffusion approximation of SGD without convexity of each loss function.
Peer effects, in which the behavior of an individual is affected by the behavior of their peers, are posited by multiple theories in the social sciences. Other processes can also produce behaviors that are correlated in networks and groups, thereby generating debate about the credibility of observational (i.e. nonexper…
An exclusion particle model is considered as a highly simplified model of a limit order market. Its price behavior reproduces the well known crossover from over-diffusion (Hurst exponent H>1/2) to diffusion (H=1/2) when the time horizon is increased, provided that orders are allowed to be canceled. For early times a ma…
A new clustering method uses diffusion processes to reveal hidden structures in data.
problem Clustering data with multimodal, nonlinear densities.
method Combines graph-based diffusion geometry with density estimation techniques.
result Proves sufficient conditions for the accuracy of the LUND procedure.
The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the cubic law of returns and the diffusive behavior of stock prices at the transaction level. However, the volatility (defined by absolute return) in the MF…
Anomalous diffusion and long-range memory in the scaled voter modelcond-mat.stat-mech
Analyzed a generalized voter model with power-law herding intensity, revealing anomalous diffusion and long-range memory.
problem Anomalous diffusion and long-range memory in a generalized voter model.
method Derived analytical expressions for moments and first passage time distribution, confirmed numerically.
result The model exhibits long-range memory indicators despite being a Markov model.
The paper shows that energy futures yield curves have an affine geometry.
problem Estimating dynamic behavior of yield curves from data while avoiding arbitrage.
method Finite dimensional models for yield curves, diffusion coefficients, and compatibility conditions.
result The compatibility of yield curves with diffusion coefficients forces an affine geometry.
New framework analyzes regret in guided diffusion for optimizing structured inputs.
problem Understanding regret behavior in guided-diffusion black-box optimization for structured design problems.
method Developed a certificate-based expected simple-regret framework that avoids assumptions breaking down in modern diffusion BO pipelines.
result Explains how exponential and polynomial convergence can arise from mass lift in near-optimal designs.
A (reactive) lattice-gas approach to economic cyclescond-mat.stat-mech
A microscopic approach to macroeconomic features is intended. A model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed. A birth-death lattice gas model taking into account the influence of an economic environment on the fitness and concentration evolution of economic entities is nu…
We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak …