S. Asmussen and H. Hering. Branching Processes. Birkhauser, 1983. Home/Search Document Not in Database Summary Related Articles Check |
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On random graph homomorphisms into Z - Benjamini, Häggström, Mossel (1998) (1 citation) (Correct)
....paths of length k. In Section 4, we treat the more intricate case where G is an n level regular tree wired at the n th level, i.e. with all leaves on the last level connected to an additional single vertex. This is tantamount to conditioning a branching random walk (see e.g. Asmussen and Hering [2] or Ney [17] on the event that all particles occupy the same location at time n 1. Somewhat surprisingly, it turns out (Theorem 4.1) that the expected range of this process is as small as O(log n) in contrast, it is well known and easy to see that the unconditional branching random walk (i.e. ....
Asmussen, S. and Hering, H. (1983) Branching Processes, Birkhauser, Boston.
Branching Processes in Quantum Electronics - Teich, Saleh (2000) (Correct)
....(electrons and holes) rather than with photons [5] Indeed, the very first application of branching process theory to the field of quantum electronics was set forth in the context of photodetection. In 1938, when branching processes first found their way into the physical sciences [1] 6] [7], 8] Shockley and Pierce [9] used a branching process model to calculate the gain and noise properties of the electron multiplication cascade in a photomultiplier tube (PMT) The branching theory descriptions of these three devices characterize not only the physics underlying their operation, ....
S. Asmussen and H. Hering, Branching Processes. Boston, MA: Birkhuser, 1983.
The Galton-Watson tree conditioned on its height - Geiger, Kersting (1998) (Correct)
....1 Introduction Let T denote the random family tree of a Galton Watson branching process starting with a single founding ancestor, where each particle independently has probability p k of producing k offspring. For a detailed definition and discussion of this process, we refer to [2] [1]. Regard T as a rooted planar tree with the distinguishable offspring of each vertex ordered from left to right. Let = P kp k be the mean number of children per particle and denote by Research of both authors supported by the German Research Foundation DFG y Fachbereich Mathematik, ....
Asmussen, S. and Hering, H. (1983) Branching Processes, Birkhauser, Boston.
Ergodic Theory on Galton-Watson Trees: Speed of Random.. - Lyons, Pemantle, Peres (1994) (16 citations) (Correct)
....(i.e. measurable with respect to the Theta invariant oe field) and so depends only on T . x6. Limit Uniform Measure. In this section, we sharpen Hawkes s theorem (1981) on the Holder exponent of limit uniform measure. This measure is defined as follows. According to the Seneta Heyde theorem (Asmussen and Hering 1983, Theorem II.5.1, p. 43) there exist constants c n such that c n 1 =cn m and W (T ) lim n 1 Zn =cn exists and is finite non zero a.s. Note that W (T ) 1 m X jxj=1 W (T (x) 6:1) Therefore, if we define for every vertex x 2 T UNIFT (x) W (T (x) m jxj W (T ) ....
....and is finite non zero a.s. Note that W (T ) 1 m X jxj=1 W (T (x) 6:1) Therefore, if we define for every vertex x 2 T UNIFT (x) W (T (x) m jxj W (T ) 6:2) then UNIFT is a unit flow and defines limit uniform measure on the boundary of T . The Kesten Stigum theorem (Asmussen and Hering 1983, Theorem I.2.1, p 23) which says 15 that R W (T ) dGW(T ) 0 iff R W (T ) dGW(T ) 1 iff W 0 a.s. iff E[Z 1 log Z 1 ] 1, implies that when E[Z 1 log Z 1 ] 1, the constants c n may be taken to be m n and so W may be used in place of W in (6.2) and (6.1) A theorem of Athreya ....
Asmussen, S. and Hering, H. (1983). Branching Processes. Birkhauser, Boston.
Conceptual Proofs of L log L Criteria for Mean Behavior.. - Lyons, Pemantle, Peres (1995) (2 citations) (Correct)
....this conditional distribution converges to infinity. Under a third moment assumption, parts (i) and (ii) of Theorem C are due to Kolmogorov (1938) and Yaglom (1947) respectively. For classical proofs of these theorems, the reader is referred to Athreya and Ney (1972) pp. 15 33 and 38 45 or Asmussen and Hering (1983), pp. 23 25, 58 63, and 74 76. A very short proof of the Kesten Stigum theorem, using martingale truncation, is in Tanny (1988) By using simple measure theory, we reduce the dichotomies between mean and sub mean behavior in the first two theorems to easier known dichotomies concerning the ....
....a Galton Watson process with immigration Y n . Let m : E[L] 1 be the mean of the offspring law and let Y have the same law as Y n . If E[log Y ] 1, then lim Z n =m n exists and is finite a.s. while if E[log Y ] 1, then lim sup Z n =c n = 1 a.s. for every constant c 0. Proof. (Asmussen and Hering (1983), pp. 50 51) Assume first that E[log Y ] 1. By Lemma 1.1, lim sup Y n =c n = 1 a.s. Since Z n Y n , the result follows. Now assume that E[log Y ] 1. Let Y be the oe field generated by fY k ; k 1g. Let Z n;k be the number of descendants at level n of the vertices which immigrated ....
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Asmussen, S. and Hering, H. (1983). Branching Processes. Birkhauser, Boston.
General Branching Processes with Immigration - Olofsson (1995) (Correct)
....is non degenerate if and only if the reproduction law has a nite x log x moment. The proof is based on comparing dioeerent measures on the set of trees and it turns out that a certain Galton Watson process with immigration is central. The basic theorem for such processes is the following (see Asmussen and Hering (1983)) Theorem 1.1. Consider a Galton Watson process where the ooespring law has mean m 1. Assume that Y n individuals immigrate in the nth generation and let Z n be the size of the nth generation. Let S = 1 X k=1 Y k m k : Then lim n 1 Z n =m n exists and is nite a.s. on the set fS ....
ASMUSSEN, S. and HERING, H. (1983) Branching Processes. Birkh#user, Boston.
A Random Energy Model For Size Dependence: Recurrence Vs.. - Külske (1997) (Correct)
....Theorem 2 . They are interesting in their own right and therefor stated as Theorem 4 in Chapter III. For the properties of the limiting distributions of the maxima of i.i.d. random variables we refer the reader to the classical references [LLR] Be] for branching processes see e.g. Du] AN] [AH]) Now, Theorem 2,2 is a statement about the recurrence v.s. transience of the sequence given by the maximizers ( N ) N=1;2; To understand better its behavior it is now interesting to investigate also the empirical distribution of N . Obviously it is the analogue of the empirical metastate ....
S.Asmussen, H.Hering, Branching Processes, Birkhauser, Boston, Basel, Stuttgart (1983)
When Does a Branching Process Grow Like its Mean?.. - Lyons, Pemantle, Peres (1993) (Correct)
....law with mean oe 2 =2 . If oe = 1, then Zn=n D 1. Under a third moment assumption, parts (i) and (ii) of Theorem 3 are due to Kolmogorov (1938) and Yaglom (1947) respectively. For classical proofs of these theorems, the reader is referred to Athreya and Ney (1972) pp. 15 33 and 38 45 or Asmussen and Hering (1983), pp. 23 25, 58 63, and 74 76. The condition E[L log L] 1 in Theorems 1 and 2 certainly appears technical, and previous proofs are indeed technical (i.e. they rely on detailed analysis of generating functions) However, while studying ergodic theory on Galton Watson trees (Lyons, Pemantle ....
Asmussen, S. and Hering, H. (1983). Branching Processes. Birkhauser, Boston.
On random graph homomorphisms into Z - Benjamini, Häggström, Mossel (1998) (1 citation) (Correct)
....paths of length k. In Section 4, we treat the more intricate case where G is an n level regular tree wired at the n th level, i.e. with all leaves on the last level connected to an additional single vertex. This is tantamount to conditioning a branching random walk (see e.g. Asmussen and Hering [2] or Ney [17] on the event that all particles occupy the same location at time n 1. Somewhat surprisingly, it turns out (Theorem 4.2) that the expected range of this process is as small as O(log n) in contrast, it is well known and easy to see that the unconditional branching random walk (i.e. ....
Asmussen, S. and Hering, H. (1983) Branching Processes, Birkhauser, Boston.
Estimation Of The Parameters Of A Branching Process From.. - Jacob, Peccoud (1998) (Correct)
....1, then lim j jOE 1;Fn j (mn j s) Gamma OE 1;Fn j (ms)j = 0: This result together with (5.5) imply Psi(ms) Gamma X k Psi k (s)F (k) 0: 5.6) Finally, up to a scale factor of s, there is exactly one strictly decreasing convex solution of (5.3) satisfying OE(0) 1 (th. 5. 2, chapter III, [1]) This property implies the result if we compare (5.6) with (5.3) From now on, W ff (N 0 ; F ) and ffi W ff (N 0 ; F ) will respectively denote the confidence regions of probability 1 Gamma ff of variables WN0 ;F and ffi WN0;F . Lemma 5.2 . If F = F m;oe 2 with F m;oe 2 continuous in m ....
Asmussen, S. and Hering, H. (1983) Branching Processes. Birkhauser, Boston, p. 435.
Analysis of a Recurrence Related to Critical.. - Drmota, Louchard, Yanev (2003) (Correct)
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S. Asmussen and H. Hering. Branching Processes. Birkhauser, 1983.
On random graph homomorphisms into Z - Benjamini, Häggström, Mossel (1999) (1 citation) (Correct)
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Asmussen, S. and Hering, H. (1983) Branching Processes, Birkhauser, Boston.
Analysis of a Recurrence Related to Critical Nonhomogeneous .. - Michael Drmota Guy (Correct)
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S. Asmussen and H. Hering. Branching Processes. Birkhauser, 1983.
Random Dyadic Tilings of the Unit Square - Janson, Randall, Spencer (2002) (Correct)
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Asmussen, S. and Hering, H. Branching Processes. Birkhauser, Basel, 1983.
Quasi-Stationary Measures for Discrete-State Markov Processes.. - Pakes (2001) (Correct)
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Asmussen, S. & Hering, H. (1983) Branching Processes. Birkhauser, Boston.
Random Dyadic Tilings of the Unit Square - Janson, Randall, Spencer (2001) (Correct)
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Asmussen S. & Hering H. Branching Processes. Birkhauser, Basel, 1983.
Galton-Watson Trees with the Same Mean have the Same Polar Sets - Pemantle, Peres (2 citations) (Correct)
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Asmussen, S. and Hering, H. (1983). Branching processes. Birkhauser: Boston.
A Quasi-Ergodic Theorem For Evanescent Processes - Breyer, Roberts (1997) (Correct)
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Asmussen, S. and Hering, H. (1983). Branching processes. Birkhauser, Boston.
Random Walks, Capacity, and Percolation on Trees - Lyons (1992) (Correct)
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Sren Asmussen and Heinrich Hering, Branching Processes. Birkhauser, Boston, 1983.
Seneta-Heyde norming in the Branching Random Walk - Biggins, Kyprianou (1996) (1 citation) (Correct)
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Asmussen, S. and Hering, H. (1983). Branching Processes. Birkhauser, Boston.
Galton-Watson Trees with the Same Mean have the Same Polar Sets - Pemantle, Peres (2 citations) (Correct)
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Asmussen, S. and Hering, H. (1983). Branching processes. Birkhauser: Boston.
Branching Random Walk: Seneta-Heyde norming - Biggins, Kyprianou (Correct)
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Asmussen, S. and Hering, H. (1983). Branching Processes. Birkhauser, Boston.
On the Convergence of Multi-Type Branching Processes With Varying.. - Jones (1997) (1 citation) (Correct)
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Asmussen, S. and Hering, H. (1993). Branching Processes, volume 3 of Progress in Probability.
Continuity For Multi-Type Branching Processes With Varying.. - Jones (1998) (Correct)
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Asmussen, S. and Hering, H. (1983) Branching Processes. Volume 3 of Progress in Probability. Birkhauser.
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