Andreas Søjmark, Fabrice Wunderlich
arXiv 22 Dec 2023 · Mathematics — Probability
arXiv:2312.15119 · PDF · DOI · OpenAlex · Extracted main text
We present a simple unifying treatment of a broad class of applications from statistical mechanics, econometrics, mathematical finance, and insurance mathematics, where (possibly subordinated) L\'evy noise arises as a scaling limit of some form of continuous-time random walk (CTRW). For each application, it is natural to rely on weak convergence results for stochastic integrals on Skorokhod space in Skorokhod's J1 or M1 topologies. As compared to earlier and entirely separate works, we are able to give a more streamlined account while also allowing for greater generality and providing important new insights. For each application, we first elucidate how the fundamental conclusions for J1 convergent CTRWs emerge as special cases of the same general principles, and we then illustrate how the specific settings give rise to different results for strictly M1 convergent CTRWs.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | WUNDERLICH, F (2023) Weak convergence of stochastic integrals on Skorokhod space in Skorokhod’s J1 and M1 topologies self | 1.000 | 40 | 5 | 100% |
| 2 | WUNDERLICH, F (2024) Functional weak convergence of stochastic integrals for moving averages and continuous-time random walks self | 1.000 | 9 | 5 | 100% |
| 3 | JURLEWICZ, A., KERN, P., MEERSCHAERT, M. M., SCHEFFLER, H.-P (2012) Fractional governing equations for coupled random walks | 0.874 | 5 | 2 | 100% |
| 4 | BECKER-KERN, P., MEERSCHAERT, M. M., SCHEFFLER, H.-P (2004) Limit theorems for coupled continuous time random walks | 0.843 | 3 | 3 | 100% |
| 5 | HENRY, B. I., STRAKA, P (2011) Lagging and leading coupled continuous time random walks, renewal times and their joint limits | 0.811 | 4 | 2 | 100% |
| 6 | PAULAUSKAS, V., RACHEV, S. T (1998) Cointegrated processes with infinite variance innovations | 0.693 | 9 | 1 | 100% |
| 7 | SCALAS, E., VILES, N (2014) A functional limit theorem for stochastic integrals driven by a time-changed symmetric $$-stable Lévy process | 0.693 | 5 | 1 | 100% |
| 8 | JACQUIER, A., TORRICELLI, L (2020) Anomalous diffusions in option prices: connecting trade duration and the volatility term structure | 0.644 | 4 | 1 | 100% |
| 9 | KURTZ, T. G., PROTTER, P. E (1991) Weak limit theorems for stochastic integrals and stochastic differential equations | 0.644 | 4 | 1 | 100% |
| 10 | WHITT, W., Glynn, Peter W., Robinson, Stephen M (2002) Stochastic-process limits. An introduction to stochastic-process limits and their application to queues. | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 37 scored citations.