Derives leading asymptotics for collision-time tails of integrable inhomogeneous Markov chains via steepest-descent analysis and Karlin-McGregor expansion, confirming a prediction for push-block particle systems.
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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.
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.
Profile MLE for the regime-switching threshold in null-recurrent diffusion converges at rate n^{-(1+γ)/2} to the arg sup of a doubly stochastic drifted Poisson process involving local time of oscillating Brownian motion.
Defines resilience evaluation D^ρ π as the L1-limit of scaled dynamic risk measure applied to process increments, and derives its dual representation as worst-case conditional expectation of an effective drift when ρ arises from BSDEs with Lipschitz or quadratic drivers.
Characterizes duals of white-noise-driven continuous stochastic flows by explicit SDEs and introduces a self-dual polynomially self-repelling flow model.
Proves existence of self-intersection local times and a change-of-variable formula for Volterra Gaussian processes inside stochastic flows with interaction, plus asymptotics and results for unbounded weights.
Introduces lifted Schrödinger bridges for Gaussian mixtures via component labels, identifying a projection gap that creates a path-space obstruction to the direct bridge.
Proves well-posedness and unique invariant measure (delta at 0 plus gamma density) for sticky CIR, derives Green's function for exact sampling, and analyzes MH and ULA samplers with explicit bias for the potential case via Girsanov.
A renormalization-group-inspired scale-splitting algorithm generates hierarchical formulas for dynamics in large dilute chemical reaction networks, illustrated on the formose reaction.
Constructs strong invariance principles and shared probability spaces for Markov chains converging to diffusions and perturbations, achieving high-probability exact coincidence on discrete grids and small deviation control under bounded coefficients.
General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.
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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.