Abstract
Shot noise processes and random fields with long memory are discussed. Convergence of the distribution of integrated polynomials of shot noise process with long memory to a self-similar process expressed as multiple Wiener-Ito integral is proved. Asymptotical normality of solutions of the Burgers equation in R 3 with random initial data as the gradient of a shot noise field with long memory is established, extending recent results by Bulinskii and Molchanov.
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Giraitis, L., Molchanov, S.A., Surgailis, D. (1993). Long Memory Shot Noises and Limit Theorems with Application to Burgers’ Equation. In: Brillinger, D., Caines, P., Geweke, J., Parzen, E., Rosenblatt, M., Taqqu, M.S. (eds) New Directions in Time Series Analysis. The IMA Volumes in Mathematics and its Applications, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9296-5_9
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DOI: https://doi.org/10.1007/978-1-4613-9296-5_9
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