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| Content Provider | Springer Nature Link |
|---|---|
| Author | Fleischmann, Klaus Klenke, Achim Xiong, Jie |
| Copyright Year | 2006 |
| Abstract | Consider the one-dimensional catalytic super-Brownian motion X (called the reactant) in the catalytic medium $$\varrho$$ which is an autonomous classical super-Brownian motion. We characterize $$(\varrho ,X)$$ both in terms of a martingale problem and (in dimension one) as solution of a certain stochastic partial differential equation. The focus of this paper is for dimension one the analysis of the longtime behavior via a mass-time-space rescaling. When scaling time by a factor of K, space is scaled by K $^{η}$ and mass by K $^{−η}$. We show that for every parameter value η ≥ 0 the rescaled processes converge as K→ ∞ in path space. While the catalyst’s limiting process exhibits a phase transition at η = 1, the reactant’s limit is always the same degenerate process. |
| Starting Page | 557 |
| Ending Page | 588 |
| Page Count | 32 |
| File Format | |
| ISSN | 08949840 |
| Journal | Journal of Theoretical Probability |
| Volume Number | 19 |
| Issue Number | 3 |
| e-ISSN | 15729230 |
| Language | English |
| Publisher | Kluwer Academic Publishers-Plenum Publishers |
| Publisher Date | 2006-10-26 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Catalyst reactant superprocess martingale problem stochastic equation density field collision measure collision local time extinction critical scaling convergence in path space Statistics Probability Theory and Stochastic Processes |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistics and Probability Statistics, Probability and Uncertainty |
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