Weak approximation of the complex Brownian sheet from a L 'evy sheet and\n applications to SPDEs

2019/07/18 by Xavier Bardina, Bardina, Xavier, Juan Pablo Márquez +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Financial Risk and Volatility Modeling #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1907.08117

Abstract

We consider a L 'evy process in the plane and we use it to construct a family\nof complex-valued random fields that we show to converge in law, in the space\nof continuous functions, to a complex Brownian sheet. We apply this result to\nobtain weak approximations of the random field solution to a semilinear\none-dimensional stochastic heat equation driven by the space-time white noise.\n

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• Kac-Stroock type approximations for the Brownian motion

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