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On the short time asymptotic of the stochastic Allen–Cahn equation

Hendrik Weber (2010)

Annales de l'I.H.P. Probabilités et statistiques

A description of the short time behavior of solutions of the Allen–Cahn equation with a smoothened additive noise is presented. The key result is that in the sharp interface limit solutions move according to motion by mean curvature with an additional stochastic forcing. This extends a similar result of Funaki [Acta Math. Sin (Engl. Ser.)15 (1999) 407–438] in spatial dimension n=2 to arbitrary dimensions.

On the singular limit of solutions to the Cox-Ingersoll-Ross interest rate model with stochastic volatility

Beáta Stehlíková, Daniel Ševčovič (2009)

Kybernetika

In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox–Ingersoll–Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of a solution...

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