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.
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.
A renormalization-group-inspired scale-splitting algorithm generates hierarchical formulas for dynamics in large dilute chemical reaction networks, illustrated on the formose reaction.
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.
Strong couplings are built for Markov chains weakly converging to diffusions, maximizing exact coincidence probability on time grids for non-degenerate and degenerate cases under bounded coefficients.
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Non-colliding space-time inhomogeneous Markov chains
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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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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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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Self-organized regime switching in null-recurrent dynamics
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.
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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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Self-intersection local times for Volterra Gaussian processes in stochastic flows with interaction
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.
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Hierarchical models for large chemical reaction networks
A renormalization-group-inspired scale-splitting algorithm generates hierarchical formulas for dynamics in large dilute chemical reaction networks, illustrated on the formose reaction.
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Convergence rate of the occupation measure of classes of ergodic processes toward their invariant distribution in mean Wasserstein distance
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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Strong Approximations for Markov Chains Weakly Converging to Diffusions
Strong couplings are built for Markov chains weakly converging to diffusions, maximizing exact coincidence probability on time grids for non-degenerate and degenerate cases under bounded coefficients.
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