References

1. Billingsley, Patrick. Convergence of probability measures.John Wiley & Sons, Inc., New York-London-Sydney 1968 xii+253 pp. MR0233396 (38 #1718)
2. Birkner, Matthias; Zähle, Iljana. A functional CLT for the occupation time of a state-dependent branching random walk. Ann. Probab. 35 (2007), no. 6, 2063--2090. MR2353383 (2008m:60198)
3. Bojdecki, T.; Gorostiza, L. G.; Ramaswamy, S. Convergence of ${scr S}'$-valued processes and space-time random fields. J. Funct. Anal. 66 (1986), no. 1, 21--41. MR0829374 (87k:60111)
4. Bojdecki. T, Gorostiza L.G. and Talarczyk. A, Sub-fractional Brownian motion and its relation to occupation times, Stat. Prob. Lett. 69, (2004), 405-419.
5. Bojdecki, T.; Gorostiza, L. G.; Talarczyk, A. Limit theorems for occupation time fluctuations of branching systems. I. Long-range dependence. Stochastic Process. Appl. 116 (2006), no. 1, 1--18. MR2186101 (2007b:60083)
6. Bojdecki, T.; Gorostiza, L. G.; Talarczyk, A. Limit theorems for occupation time fluctuations of branching systems. II. Critical and large dimensions. Stochastic Process. Appl. 116 (2006), no. 1, 19--35. MR2186102 (2007b:60084)
7. Bojdecki, Tomasz; Gorostiza, Luis G.; Talarczyk, Anna. A long range dependence stable process and an infinite variance branching system. Ann. Probab. 35 (2007), no. 2, 500--527. MR2308586 (2008h:60344)
8. Bojdecki, Tomasz; Gorostiza, Luis G.; Talarczyk, Anna. Occupation time fluctuations of an infinite-variance branching system in large dimensions. Bernoulli 13 (2007), no. 1, 20--39. MR2307392 (2008g:60094)
9. Bojdecki, T.; Gorostiza, L. G.; Talarczyk, A. Occupation time limits of inhomogeneous Poisson systems of independent particles. Stochastic Process. Appl. 118 (2008), no. 1, 28--52. MR2376251 (2009e:60077)
10. Bojdecki, Tomasz; Gorostiza, Luis G.; Talarczyk, Anna. Self-similar stable processes arising from high-density limits of occupation times of particle systems. Potential Anal. 28 (2008), no. 1, 71--103. MR2366400 (2009c:60119)
11. Breiman, Leo. Probability.Addison-Wesley Publishing Company, Reading, Mass.-London-Don Mills, Ont. 1968 ix+421 pp. MR0229267 (37 #4841)
12. Cohen, Serge; Samorodnitsky, Gennady. Random rewards, fractional Brownian local times and stable self-similar processes. Ann. Appl. Probab. 16 (2006), no. 3, 1432--1461. MR2260069 (2008b:60080)
13. Cox, J. Theodore; Griffeath, David. Occupation times for critical branching Brownian motions. Ann. Probab. 13 (1985), no. 4, 1108--1132. MR0806212 (87h:60102)
14. Dawson, Donald A. Measure-valued Markov processes. École d'Été de Probabilités de Saint-Flour XXI---1991, 1--260, Lecture Notes in Math., 1541, Springer, Berlin, 1993. MR1242575 (94m:60101)
15. Dawson, D. A.; Gorostiza, L. G.; Wakolbinger, A. Occupation time fluctuations in branching systems. J. Theoret. Probab. 14 (2001), no. 3, 729--796. MR1860521 (2002h:60183)
16. Dawson, Donald A.; Perkins, Edwin A. Historical processes. Mem. Amer. Math. Soc. 93 (1991), no. 454, iv+179 pp. MR1079034 (92a:60145)
17. Dawson, Donald A.; Perkins, Edwin A. Measure-valued processes and renormalization of branching particle systems. Stochastic partial differential equations: six perspectives, 45--106, Math. Surveys Monogr., 64, Amer. Math. Soc., Providence, RI, 1999. MR1661763 (2000a:60098)
18. Deuschel, Jean-Dominique; Rosen, Jay. Occupation time large deviations for critical branching Brownian motion, super-Brownian motion and related processes. Ann. Probab. 26 (1998), no. 2, 602--643. MR1626503 (99g:60057)
19. Dong, Zhao; Feng, Shui. Occupation time processes of super-Brownian motion with cut-off branching. J. Appl. Probab. 41 (2004), no. 4, 984--997. MR2122474 (2006b:60184)
20. Theory and applications of long-range dependence.Edited by Paul Doukhan, George Oppenheim and Murad S. Taqqu.Birkhäuser Boston, Inc., Boston, MA, 2003. xii+719 pp. ISBN: 0-8176-4168-8 MR1956041 (2003h:60004)
21. Engländer, János; Kyprianou, Andreas E. Local extinction versus local exponential growth for spatial branching processes. Ann. Probab. 32 (2004), no. 1A, 78--99. MR2040776 (2005k:60270)
22. Etheridge, Alison M. An introduction to superprocesses.University Lecture Series, 20. American Mathematical Society, Providence, RI, 2000. xii+187 pp. ISBN: 0-8218-2706-5 MR1779100 (2001m:60111)
23. Fleischmann, Klaus; Gärtner, Jürgen. Occupation time processes at a critical point. Math. Nachr. 125 (1986), 275--290. MR0847367 (88b:60230)
24. Vakolbinger, A.; Vatutin, V. A.; Flyaĭshmann, K. Branching systems with long-lived particles at a critical dimension.(Russian) Teor. Veroyatnost. i Primenen. 47 (2002), no. 3, 417--451; translation in Theory Probab. Appl. 47 (2003), no. 3, 429--454 MR1975423 (2004i:60125)
25. Gorostiza, L. G.; López-Mimbela, J. A. An occupation time approach for convergence of measure-valued processes, and the death process of a branching system. Statist. Probab. Lett. 21 (1994), no. 1, 59--67. MR1309877 (95i:60040)
26. Gorostiza, Luis G.; Navarro, Reyla; Rodrigues, Eliane R. Some long-range dependence processes arising from fluctuations of particle systems. Acta Appl. Math. 86 (2005), no. 3, 285--308. MR2136367 (2006d:60064)
27. Gorostiza, Luis G.; Wakolbinger, Anton. Persistence criteria for a class of critical branching particle systems in continuous time. Ann. Probab. 19 (1991), no. 1, 266--288. MR1085336 (91k:60089)
28. Heyde, C. C.; Yang, Y. On defining long-range dependence. J. Appl. Probab. 34 (1997), no. 4, 939--944. MR1484026 (98j:60055)
29. Heyde, C. C. On modes of long-range dependence. J. Appl. Probab. 39 (2002), no. 4, 882--888. MR1938178 (2003j:60046)
30. Hambly, Ben; Jones, Liza. Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric $alpha$-stable processes. Electron. J. Probab. 12 (2007), no. 30, 862--887 (electronic). MR2318413 (2008g:60144)
31. Hong, Wenming. Longtime behavior for the occupation time process of a super-Brownian motion with random immigration. Stochastic Process. Appl. 102 (2002), no. 1, 43--62. MR1934154 (2003m:60240)
32. Houdré, Christian; Villa, José. An example of infinite dimensional quasi-helix. Stochastic models (Mexico City, 2002), 195--201, Contemp. Math., 336, Amer. Math. Soc., Providence, RI, 2003. MR2037165 (2004m:60077)
33. Iscoe, I. A weighted occupation time for a class of measure-valued branching processes. Probab. Theory Relat. Fields 71 (1986), no. 1, 85--116. MR0814663 (87c:60070)
34. Iscoe, I. On the supports of measure-valued critical branching Brownian motion. Ann. Probab. 16 (1988), no. 1, 200--221. MR0920265 (88j:60097)
35. Iscoe, Ian; Lee, Tzong-Yow. Large deviations for occupation times of measure-valued branching Brownian motions. Stochastics Stochastics Rep. 45 (1993), no. 3-4, 177--209. MR1306931 (96a:60027)
36. Kaj I. and Taqqu M. S, Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach. In and Out of Equilibrium 2. Eds. M. E. Vares, V. Sidoravicius. Progress in Probability, Vol. 60, 383-427. Birkhauser, 2008.
37. Klenke, Achim. Clustering and invariant measures for spatial branching models with infinite variance. Ann. Probab. 26 (1998), no. 3, 1057--1087. MR1634415 (99i:60160)
38. Lee, Tzong-Yow; Remillard, Bruno. Large deviations for the three-dimensional super-Brownian motion. Ann. Probab. 23 (1995), no. 4, 1755--1771. MR1379167 (96m:60067)
39. Levy, Joshua B.; Taqqu, Murad S. Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards. Bernoulli 6 (2000), no. 1, 23--44. MR1781180 (2001f:60023)
40. Li, Zenghu; Zhou, Xiaowen. Distribution and propagation properties of superprocesses with general branching mechanisms. Commun. Stoch. Anal. 2 (2008), no. 3, 469--477. MR2485004
41. Maejima, Makoto; Yamamoto, Kenji. Long-memory stable Ornstein-Uhlenbeck processes. Electron. J. Probab. 8 (2003), no. 19, 18 pp. (electronic). MR2041820 (2005c:60076)
42. Méléard, S.; Roelly, S. An ergodic result for critical spatial branching processes. Stochastic analysis and related topics (Silivri, 1990), 333--341, Progr. Probab., 31, Birkhäuser Boston, Boston, MA, 1992. MR1203380 (93m:60172)
43. Miƚoś, Piotr. Occupation time fluctuations of Poisson and equilibrium finite variance branching systems. Probab. Math. Statist. 27 (2007), no. 2, 181--203. MR2445992 (Review)
44. Milos, P. Occupation time fluctuations of Poisson and equilibrium branching systems in critical and large dimensions, Probab. Math. Statist. 28 (2), (2008), 235-256.
45. Milos, P. Occupation time fluctuation limits of infinite variance equilibrium branching systems, (preprint), Math. ArXiv. PR 0802.0187.
46. Mitoma, Itaru. Tightness of probabilities on $C([0,1];{cal S}sp{prime} )$ and $D([0,1];{cal S}sp{prime} )$. Ann. Probab. 11 (1983), no. 4, 989--999. MR0714961 (85f:60008)
47. Perkins, Edwin. Polar sets and multiple points for super-Brownian motion. Ann. Probab. 18 (1990), no. 2, 453--491. MR1055416 (91i:60109)
48. Perkins, Edwin. Dawson-Watanabe superprocesses and measure-valued diffusions. Lectures on probability theory and statistics (Saint-Flour, 1999), 125--324, Lecture Notes in Math., 1781, Springer, Berlin, 2002. MR1915445 (2003k:60104)
49. Pipiras, Vladas; Taqqu, Murad S.; Levy, Joshua B. Slow, fast and arbitrary growth conditions for renewal-reward processes when both the renewals and the rewards are heavy-tailed. Bernoulli 10 (2004), no. 1, 121--163. MR2044596 (2005e:60198)
50. Rosiński, Jan; Żak, Tomasz. The equivalence of ergodicity of weak mixing for infinitely divisible processes. J. Theoret. Probab. 10 (1997), no. 1, 73--86. MR1432616 (97m:60044)
51. Samorodnitsky, Gennady. Long range dependence. Found. Trends Stoch. Syst. 1 (2006), no. 3, 163--257. ISBN: 978-1-60198-090-8 MR2379935
52. Samorodnitsky, Gennady; Taqqu, Murad S. Stable non-Gaussian random processes.Stochastic models with infinite variance.Stochastic Modeling. Chapman & Hall, New York, 1994. xxii+632 pp. ISBN: 0-412-05171-0 MR1280932 (95f:60024)
53. Shiozawa, Yuichi. Extinction of branching symmetric $alpha$-stable processes. J. Appl. Probab. 43 (2006), no. 4, 1077--1090. MR2274638 (2008e:60266)
54. Talarczyk, Anna. A functional ergodic theorem for the occupation time process of a branching system. Statist. Probab. Lett. 78 (2008), no. 7, 847--853. MR2398358 (2009c:60230)
55. Taqqu, Murad S. Fractional Brownian motion and long-range dependence. Theory and applications of long-range dependence, 5--38, Birkhäuser Boston, Boston, MA, 2003. MR1956042
56. Vakolbinger, A.; Vatutin, V. A. Branching processes in long-lived particles.(Russian) Teor. Veroyatnost. i Primenen. 43 (1998), no. 4, 655--671; translation in Theory Probab. Appl. 43 (1999), no. 4, 620--632 MR1692425 (2000e:60143)
57. Zhang, Mei. Functional central limit theorem for the super-Brownian motion with super-Brownian immigration. J. Theoret. Probab. 18 (2005), no. 3, 665--685. MR2167646 (2007e:60086)
58. Zhou, Xiaowen. A zero-one law of almost sure local extinction for $(1+beta)$-super-Brownian motion. Stochastic Process. Appl. 118 (2008), no. 11, 1982--1996. MR2462283