Mixing Properties of Multivariate Infinitely Divisible Random Fields

Barndorff-Nielsen, O.E., Benth, F.E., Veraart, A.E.D.: Recent Advances in Ambit Stochastics with a View Towards Tempo-Spatial Stochastic Volatility/Intermittency, vol. 104, pp. 25–60. Banach Center Publications, Warszawa (2014)

Barndorff-Nielsen, O.E., Schmiegel, J.: Lévy-based tempo-spatial modelling; with applications to turbulence. Uspekhi Mat. Nauk 159, 63–90 (2004)

Barndorff-Nielsen, O.E., Schmiegel, J.: Ambit processes: with applications to turbulence and tumour growth. In: Stochastic Analysis and Applications: The Abel Symposium 2005, pp. 93–124. Springer (2007)

Barndorff-Nielsen, O.E., Pedersen, J.: Meta times and extended subordination. Theory Probab. Appl. 56(2), 319–327 (2012)

Cuppens, R.: Decomposition of Multivariate Distributions. Academic Press, New York (1975)

Fuchs, F., Stelzer, R.: Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model. ESAIM Probab. Stat. 17, 455–471 (2013)

Gross, A.: Some mixing conditions for stationary symmetric stable stochastic processes. Stoch. Process. Appl. 51, 277–295 (1994)

Jónsdóttir, K., Rønn-Nielsen, A., Mouridsen, K., Vedel Jensen, E.: Lévy-based modelling in brain imaging. Scand. J. Stat. 40(3), 511–529 (2013)

Kokoszka, P., Taqqu, M.S.: A characterization of mixing processes of type G. J. Theor. Probab. 9, 3–17 (1996)

Magdziarz, M.: A note on Maruyama’s mixing theorem. Theory Probab. Appl. 54, 322–324 (2010)

Maruyama, G.: Infinitely divisible processes. Theory Probab. Appl. 15, 1–22 (1970)

Rajput, B.S., Rosinski, J.: Spectral representations of infinitely divisible processes. Probab. Theory Relat. Fields 82, 451–487 (1989)

Rosinski, J., Zak, T.: Simple conditions for mixing of infinitely divisible processes. Stoch. Process. Appl. 61, 277–288 (1996)

Rosinski, J., Zak, T.: The equivalence of ergodicity and weak mixing for infinitely divisible processes. J. Theor. Probab. 10(1), 73–86 (1997)

Roy, E.: Ergodic properties of Poissonian ID processes. Ann. Probab. 35, 551–576 (2007)

Roy, E.: Poisson suspensions and infinite ergodic theory. Ergod. Theory Dyn. Syst. 29, 667–683 (2009)

Roy, P.: Nonsingular group actions and stationary S $$\alpha $$ α S random fields. Proc. Am. Math. Soc. 138, 2195–2202 (2010)

Roy, P., Samorodnitsky, G.: Stationary symmetric $$\alpha $$ α -stable discrete parameter random fields. J. Theor. Probab. 21, 212–233 (2008)

Sato, K.: Lévy Processes and Infinitely Divisible Distributions, Volume 68 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1999)

Surgailis, D., Rosinski, J., Mandrekar, V., Cambanis, S.: Stable mixed moving averages. Probab. Theory Relat. Fields 97(4), 543–558 (1993)

Veraart, A.E.D.: Stationary and multi-self-similar random fields with stochastic volatility. Stochastics 87(5), 848–870 (2015)

Wang, Y., Roy, P., Stoev, S.A.: Ergodic properties of sum- and max-stable stationary random fields via null and positive group actions. Ann. Probab. 41(1), 206–228 (2013)