The sticky CIR process on [0,∞) has a unique invariant measure that mixes a point mass at zero with a gamma-type density, and admits an exact sampler via an explicit Green's function in the zero-potential case.
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Continuous Martingales and Brownian Motion
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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.
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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Sticky CIR process with potential: invariant measure and exact sampling
The sticky CIR process on [0,∞) has a unique invariant measure that mixes a point mass at zero with a gamma-type density, and admits an exact sampler via an explicit Green's function in the zero-potential case.
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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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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.