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Asymptotic behaviour and functional limit theorems for a time changed Wiener process

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FD2W02 - Fractional kinetics, hydrodynamic limits and fractals

This is a joint talk with Yuri Kondratiev and Rene Schilling.  We present     a bit unexpected version of dynamic system in the random media. Namely, we study the asymptotic behavior of the properly normalized time-changed Wiener processes  with a specific time change which transformed its generator multiplying it by some intensity. Applying functional limit theorem for the superposition of stochastic processes, we prove the limit theorems for the normalized time-changed Wiener process, with different normalization, depending on the asymptotics of intensity. As one of possible limits, we get a skew Brownian motion.

This talk is part of the Isaac Newton Institute Seminar Series series.

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