The stability of the multivariate geometric Brownian motion as a bilinear matrix inequality problem

Autor:	Barrera, Gerardo, Bjarkason, Eyleifur, Hafstein, Sigurdur
Rok vydání:	2024
Předmět:	Mathematics - Probability Mathematics - Numerical Analysis Mathematics - Optimization and Control 60H10 93D05 93D30 34F05 37H30 93D23
Druh dokumentu:	Working Paper
Popis:	In this manuscript, we study the stability of the origin for the multivariate geometric Brownian motion. More precisely, under suitable sufficient conditions, we construct a Lyapunov function such that the origin of the multivariate geometric Brownian motion is globally asymptotically stable in probability. Moreover, we show that such conditions can be rewritten as a Bilinear Matrix Inequality (BMI) feasibility problem. We stress that no commutativity relations between the drift matrix and the noise dispersion matrices are assumed and therefore the so-called Magnus representation of the solution of the multivariate geometric Brownian motion is complicated. In addition, we exemplify our method in numerous specific models from the literature such as random linear oscillators, satellite dynamics, inertia systems, diagonal noise systems, cancer self-remission and smoking. Comment: 34 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.16765 Zobrazit plný text záznamu View this record from Arxiv