Proves temporal convergence rate of almost 1 for stochastic-convolution-based approximations of nonlinear 1+1D SPDEs with additive space-time white noise, improving on the optimal 1/4 rate for Wiener-increment schemes.
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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.
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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Higher order approximation of nonlinear SPDEs with additive space-time white noise
Proves temporal convergence rate of almost 1 for stochastic-convolution-based approximations of nonlinear 1+1D SPDEs with additive space-time white noise, improving on the optimal 1/4 rate for Wiener-increment schemes.
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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.