The stability of the multivariate geometric Brownian motion as a bilinear matrix inequality problem
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909621502869504 |
|---|---|
| author | Barrera, Gerardo Bjarkason, Eyleifur Hafstein, Sigurdur |
| author_facet | Barrera, Gerardo Bjarkason, Eyleifur Hafstein, Sigurdur |
| contents | 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 and non-diagonal noise systems, cancer self-remission and smoking. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16765 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The stability of the multivariate geometric Brownian motion as a bilinear matrix inequality problem Barrera, Gerardo Bjarkason, Eyleifur Hafstein, Sigurdur Probability Numerical Analysis Optimization and Control 60H10, 93D05, 93D30, 34F05, 37H30, 93D23 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 and non-diagonal noise systems, cancer self-remission and smoking. |
| title | The stability of the multivariate geometric Brownian motion as a bilinear matrix inequality problem |
| topic | Probability Numerical Analysis Optimization and Control 60H10, 93D05, 93D30, 34F05, 37H30, 93D23 |
| url | https://arxiv.org/abs/2403.16765 |