Diffusion posterior samplers produce biased outputs that can be expressed as an Ornstein-Uhlenbeck path expectation via a surrogate Gaussian path and Feynman-Kac representation, with STSL flattening the spatially varying bias term.
Graduate Texts in Mathematics, vol
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The second term in the spectral expansion of the expected LQG heat trace as t to 0 is governed by the KPZ exponent.
The value function is the unique minimizer of a functional whose Euler-Lagrange equation matches the HJB equation, with a verification theorem giving optimal policies via change of measure and BSDE uniqueness.
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
Generalized bridges with constraints solve Schrödinger problems, enabling broader financial equilibrium models with frictions and proving convergence of trading-cost equilibria to the classical Kyle model.
Derives Õ(d β² A² / ε⁴) oracle complexity for AIS estimating normalizing constant Z to relative error ε and introduces reverse diffusion sampler for geometric paths with large action.
Existence is proved of a slowed-down sticky Brownian motion that induces a MAXCUT rounding attaining the Goemans-Williamson approximation ratio.
Characterizes duals of white-noise-driven continuous stochastic flows by explicit SDEs and introduces a self-dual polynomially self-repelling flow model.
Adapts hybrid LSMC-PDE framework to the GDMR model for Bermudan option pricing and reports lower errors than plain LSMC in numerical experiments with low to moderate simulation paths.
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Diffusion-Based Posterior Sampling: A Feynman-Kac Analysis of Bias and Stability
Diffusion posterior samplers produce biased outputs that can be expressed as an Ornstein-Uhlenbeck path expectation via a surrogate Gaussian path and Feynman-Kac representation, with STSL flattening the spatially varying bias term.
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Spectral expansion of LQG heat trace and KPZ scaling
The second term in the spectral expansion of the expected LQG heat trace as t to 0 is governed by the KPZ exponent.
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Infinite Horizon Optimal Consumption: Intertemporal Hedging under Epstein-Zin Preferences
The value function is the unique minimizer of a functional whose Euler-Lagrange equation matches the HJB equation, with a verification theorem giving optimal policies via change of measure and BSDE uniqueness.
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Sinkhorn Treatment Effects: A Causal Optimal Transport Measure
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
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Schr\"odinger's problem with constraints
Generalized bridges with constraints solve Schrödinger problems, enabling broader financial equilibrium models with frictions and proving convergence of trading-cost equilibria to the classical Kyle model.
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Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond
Derives Õ(d β² A² / ε⁴) oracle complexity for AIS estimating normalizing constant Z to relative error ε and introduces reverse diffusion sampler for geometric paths with large action.
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Krivine diffusions attain the Goemans--Williamson approximation ratio
Existence is proved of a slowed-down sticky Brownian motion that induces a MAXCUT rounding attaining the Goemans-Williamson approximation ratio.
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Continuous stochastic flows driven by white noise and their duals
Characterizes duals of white-noise-driven continuous stochastic flows by explicit SDEs and introduces a self-dual polynomially self-repelling flow model.
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A Hybrid LSMC-PDE Method for Bermudan Option Pricing under the Gatheral Double Mean-Reverting Model
Adapts hybrid LSMC-PDE framework to the GDMR model for Bermudan option pricing and reports lower errors than plain LSMC in numerical experiments with low to moderate simulation paths.
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