Measure change in multitype branching

By J. Biggins, Andreas E. Kyprianou. Advances in Applied Probability, 2004

247 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/db1d2f70385ada580e180ed57c3c42ed39c690c6

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Citations in the corpus

The functional equation of the smoothing transform (2009, background): “This notion indicates that the above defined random sets are special optional lines in the sense of Jagers [28], Kyprianou [31] and Biggins and Kyprianou [15], but where, additionally, stopping along any path of the infinite tree V follows the same stopping rule.”
A Log-Type Moment Result for Perpetuities and Its Application to Martingales in Supercritical Branching Random Walks (2008, methodology): “The last inequality has also been obtained by Biggins and Kyprianou, see [8], p.”
Survival probabilities for branching Brownian motion with absorption (2007, background): “For full details of the construction of such changes of measure we refer the reader to the spine theory given in Hardy and Harris [11], but also see Chauvin and Rouault [6], and Kyprianou [18].”
Convergence in law of the minimum of a branching random walk (2013, unknown): “[6] Biggins, J.”
The Seneta–Heyde scaling for the branching random walk (2011, methodology): “(The positiveness of D∞ was proved in [12] under slightly stronger assumptions.”
Convergence in Law for the Branching Random Walk Seen from Its Tip (2011, methodology): “With a slight extension of [8], equality (5.”
Critical Gaussian multiplicative chaos: Convergence of the derivative martingale (2012, methodology): “These tools have already been introduced in the context of discrete multiplicative cascade models in order to study the corresponding derivative martingale; see [15].”
Elementary fixed points of the BRW smoothing transforms with infinite number of summands (2003, methodology): “Fixed points of the BRW smoothing transforms with almost surely finite number of summands were studied (without using the name) by Biggins (1977), Biggins and Kyprianou (1996, 1997, 2001, 2003), Kyprianou (1998), Liu (2000).”
Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees (2007, background): “If 0 β 1, the study of W n,β boils down to the case ψ ′ (1) 0, which was investigated by Biggins and Kyprianou [7].”
Discretization Methods for Homogeneous Fragmentations (2004, methodology): “For the branching random walk, it has been considered by Kyprianou [18], Liu [20] with the help of a functional equation and by Biggins and Kyprianou [10] with the measure change method.”
A Spine Approach to Branching Diffusions with Applications to L p -Convergence of Martingales (2009, methodology): “Much of the notation that we use for the underlying space of trees, the filtrations and the measures is closely related to that found in Kyprianou [40].”
Martingales and Profile of Binary Search Trees (2004, unknown): “This method is usual and fruitful in modern developments on branching processes, and also in the study of fragmentation processes ([9, 14, 30]).”
Branching random walks (2015, methodology): “5, first proved by Biggins and Kyprianou [57] under slightly stronger assumptions, are borrowed from Äıdékon [8].”
Fixed Points of the Smoothing Transform: the Boundary Case (2005, background): “= c ∈ (0,∞); (5) furthermore P (∆ = 0) = 1 if and only if (− logψ)L(ψ)→∞ as ψ ↓ 0.”
Convergence in law of the minimum of a branching random walk (2011, methodology): “We adapt the proof of [7]; see [22] for the case of the additive martingale.”
Further probabilistic analysis of the Fisher–Kolmogorov–Petrovskii–Piscounov equation: one sided travelling-waves (2006, background): “For a detailed setup and notation for these changes of measure and spine decompositions in branching Brownian motion the reader should refer to the recent new approach presented in Hardy and Harris [17], in addition to Kyprianou [27] and Chauvin and Rouault [9].”
Gaussian multiplicative chaos and applications: A review (2013, background): “Such an object has been intensively studied in the case of multiplicative cascades, branching random walks [28, 98] or branching Brownian motions [116].”