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Limit theorems for marked dynamic contagion processes with mean-reverting Cox–Ingersoll–Ross intensity

Author

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  • Pandey, Shamiksha
  • Selvamuthu, Dharmaraja

Abstract

In this paper, we introduce and study the marked dynamic contagion process, where the intensity process is governed by the Cox–Ingersoll–Ross (CIR) model. This framework extends both the Hawkes and the Cox process with Poisson shot-noise intensity by incorporating self-exciting and externally-exciting jumps, and random noise. This allows to capture the effects of events caused by internal (endogenous) and external (exogenous) factors, along with random fluctuations of the market. Furthermore, the process includes an independent and identically distributed (i.i.d.) sequence of marks, which represent distinct event characteristics and influence the timing and behavior of subsequent occurrences. For the proposed model, we examine the theoretical properties, including the Law of Large Numbers (LLN), the Central Limit Theorem (CLT), and the Large Deviation Principle (LDP).

Suggested Citation

  • Pandey, Shamiksha & Selvamuthu, Dharmaraja, 2026. "Limit theorems for marked dynamic contagion processes with mean-reverting Cox–Ingersoll–Ross intensity," Statistics & Probability Letters, Elsevier, vol. 235(C).
    • Handle: RePEc:eee:stapro:v:235:y:2026:i:c:s0167715226000933
    DOI: 10.1016/j.spl.2026.110729
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