Asymptotic results for super-Brownian motions and semilinear differential equations

Lee, Tzong-Yow

doi:10.1090/S1079-6762-98-00048-1

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ISSN 1079-6762

Asymptotic results for super-Brownian motions and semilinear differential equations

Author: Tzong-Yow Lee
Journal: Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 56-62
MSC (1991): Primary 60B12, 60F10; Secondary 60F05, 60J15
Posted: September 14, 1998
MathSciNet review: 1641127
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Abstract: Limit laws for three-dimensional super-Brownian motion are derived, conditioned on survival up to a large time. A large deviation principle is proved for the joint behavior of occupation times and their difference. These are done via analyzing the generating function and exploiting a connection between probability and differential/integral equations.

[BCG] Maury Bramson, J. Theodore Cox, and David Griffeath, Occupation time large deviations of the voter model, Probab. Theory Related Fields 77 (1988), no. 3, 401–413. MR 931506 (89c:60116), http://dx.doi.org/10.1007/BF00319297
[CG] J. Theodore Cox and David Griffeath, Occupation times for critical branching Brownian motions, Ann. Probab. 13 (1985), no. 4, 1108–1132. MR 806212 (87h:60102)
[D] D. A. Dawson, The critical measure diffusion process, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 40 (1977), no. 2, 125–145. MR 0478374 (57 #17857)
[DG] Donald A. Dawson and Jürgen Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics 20 (1987), no. 4, 247–308. MR 885876 (89c:60092), http://dx.doi.org/10.1080/17442508708833446
[DR] Deuschel, J.-D. and Rosen, J. (1998) Occupation time large deviations for critical branching Brownian motion, super-Brownian motion and related processes. Ann. Probab. 26, no. 2, 602-643. CMP 98:13
[Dy] E. B. Dynkin, Superprocesses and their linear additive functionals, Trans. Amer. Math. Soc. 314 (1989), no. 1, 255–282. MR 930086 (89k:60124), http://dx.doi.org/10.1090/S0002-9947-1989-0930086-7
[I1] I. Iscoe, A weighted occupation time for a class of measure-valued branching processes, Probab. Theory Relat. Fields 71 (1986), no. 1, 85–116. MR 814663 (87c:60070), http://dx.doi.org/10.1007/BF00366274
[I2] I. Iscoe, Ergodic theory and a local occupation time for measure-valued critical branching Brownian motion, Stochastics 18 (1986), no. 3-4, 197–243. MR 861108 (88a:60148), http://dx.doi.org/10.1080/17442508608833409
[IL] Ian Iscoe and Tzong-Yow Lee, Large deviations for occupation times of measure-valued branching Brownian motions, Stochastics Stochastics Rep. 45 (1993), no. 3-4, 177–209. MR 1306931 (96a:60027)
[L] T.-Y. Lee, Some limit theorems for critical branching Bessel processes, and related semilinear differential equations, Probab. Theory Related Fields 84 (1990), no. 4, 505–520. MR 1042063 (91e:60245), http://dx.doi.org/10.1007/BF01198317
[LR] Tzong-Yow Lee and Bruno Remillard, Large deviations for the three-dimensional super-Brownian motion, Ann. Probab. 23 (1995), no. 4, 1755–1771. MR 1379167 (96m:60067)

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