Abstract:
We prove the multidimensional analog of the well-known Watson lemma and then apply it to prove a local limit theorem for the transition probabilities of symmetric random walks on the multidimensional lattice with infinite variance of jumps.
Keywords:
multidimensional Watson lemma, symmetric random walk, infinite variance of jumps, multidimensional lattice, branching random walk.
This study was carried out in Lomonosov Moscow State University and Steklov Mathematical Institute of Russian Academy of Sciences, and was supported by the Russian Science Foundation under grant 14-21-00162.
Citation:
A. I. Rytova, E. B. Yarovaya, “Multidimensional Watson Lemma and Its Applications”, Mat. Zametki, 99:3 (2016), 395–403; Math. Notes, 99:3 (2016), 406–412
This publication is cited in the following 9 articles:
G. A. Popov, E. B. Yarovaya, “Aggregation of states of a branching random walk over multidimensional lattice”, Moscow University Mathematics Bulletin, 79:1 (2024), 60–70
K. S. Ryadovkin, “On periodic branching random walks on $\mathbf{Z}^d$ with infinite variance of jumps”, Theory Probab. Appl., 69:1 (2024), 88–98
Rytova A., Yarovaya E., “Survival Analysis of Particle Populations in Branching Random Walks”, Commun. Stat.-Simul. Comput., 50:10 (2021), 3031–3045
A. Rytova, E. Yarovaya, “Heavy-tailed branching random walks on multidimensional lattices. A moment approach”, Proc. R. Soc. Edinb. Sect. A-Math., 151:3 (2021), PII S0308210520000463, 971–992
D. M. Balashova, “Branching random walks with alternating sign intensities of branching sources”, J. Math. Sci., 262:4 (2022), 442–451
A. I. Rytova, “Harmonic analysis of random walks with heavy tails”, J. Math. Sci., 262:4 (2022), 514–524
A. I. Rytova, E. B. Yarovaya, “Moments of the numbers of particles in a heavy-tailed branching random walk”, Russian Math. Surveys, 74:6 (2019), 1126–1128
E. Yarovaya, “Operator equations of branching random walks”, Methodol. Comput. Appl. Probab., 21:3, SI (2019), 1007–1021
“International conference on stochastic methods (Abstracts)”, Theory Probab. Appl., 62:4 (2018), 640–674
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