1 results
Self-exciting multifractional processes
- Part of
-
- Journal:
- Journal of Applied Probability / Volume 58 / Issue 1 / March 2021
- Published online by Cambridge University Press:
- 25 February 2021, pp. 22-41
- Print publication:
- March 2021
-
- Article
- Export citation
-
We propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this by means of a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as giving bounds on the p-order moments, for all
$p\geq1$. We show convergence of an Euler–Maruyama scheme for the process, and also give the rate of convergence, which is dependent on the self-exciting dynamics of the process. Moreover, we discuss various applications of this process, and give examples of different functions to model self-exciting behavior.
