Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations
Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations
复制标题
带加性核的 Smoluchowski 凝固方程的永恒解及其概率解释
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Bertoin
中科院分区：
文献类型：
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作者：
J. Bertoin
这项工作的基石部分是受到 Aldous 和 Pitman 对所谓的永恒加性聚结剂的表征的推动，它是对具有加性核的 Smoluchowski 凝固方程的一般永恒解的显式表达。该表达式指向某些没有负跳跃的 Levy 过程，更准确地说，指向基于此类过程的聚合的随机模型，该模型最近已被 Bertoin 和 Miermont 考虑，并且已知与加性合并具有密切关系。作为一个应用，我们证明了可以从随机模型的某些流体动力学极限中获得永恒解。我们还提出了一个简单的条件，确保存在永恒解的平滑密度。
The cornerstone of this work, which is partly motivated by the characterization of the so-called eternal additive coalescents by Aldous and Pitman, is an explicit expression for the general eternal solution to Smoluchowski's coagulation equation with additive kernel. This expression points at certain Levy processes with no negative jumps and more precisely at a stochastic model for aggregation based on such processes, which has been recently considered by Bertoin and Miermont and is known to bear close relations with the additive coalescence. As an application, we show that the eternal solutions can be obtained from some hydrodynamic limit of the stochastic model. We also present a simple condition that ensures the existence of a smooth density for an eternal solution.