Nonlinear stochastic ordinary and partial differential equations: regularity properties and numerical approximations
نویسنده
چکیده
In this talk we present a few recent results on regularity properties and numerical approximations for stochastic ordinary and partial differential equations with non-globally monotone nonlinearities. In particular, we establish strong convergence rates for Cox-Ingersoll-Ross (CIR) processes, stochastic Duffing-van der Pol oscillators, stochastic Lorenz equations, and Cahn-Hilliard-Cook equations. CIR processes are widely used in the financial engineering industry to estimate prices of financial derivatives. We also present a calibration result for CIR processes and stocks from the S & P 500 (Standard & Poor’s 500) stock market index. The talk is based on joint works with Martin Hairer, Martin Hutzenthaler, Thomas MuellerGronbach, Marco Noll, and Larisa Yaroslavtseva. More details on this topic can also be found at [https://www.math.ethz.ch/sam/research/projects.html?details=33]. ∗Speaker †Corresponding author: [email protected] sciencesconf.org:montecarlo16:114056
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