On monotonicity and order-preservation for multidimensional G-diffusion processes
Peng Luo, Guangyan Jia
TL;DR
This paper establishes comparison theorems and conditions for monotonicity and order-preservation in multidimensional G-diffusion processes, with applications demonstrating the theoretical results.
Contribution
It provides the first comprehensive set of necessary and sufficient conditions for monotonicity and order-preservation in multidimensional G-diffusions.
Findings
Comparison theorem for multidimensional G-SDEs proved
Necessary and sufficient conditions for monotonicity established
Applications demonstrating theoretical results included
Abstract
In this paper, we prove a comparison theorem for multidimensional G-SDEs. Moreover we obtain respectively the sufficient conditions and necessary conditions of the monotonicity and order-preservation for two multidimensional G-diffusion processes. Finally, we give some applications.
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Taxonomy
TopicsStochastic processes and financial applications · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering