Abstract. In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz conditions on their coefficients.

In this paper we will discuss the optimal risk transfer problems when risk measures are generated by G-expectations, and we present the relationship between inf-convolution of G-expectations and the inf-convolution of drivers G.Comment: 23 page

Background: It is currently estimated that about 1/3 of the global population is infected with mycobacterium tuberculosis (TB), and about 90% of those infected have asymptomatic latent infections.It has been reported that 85-90% of newly diagnosed active TB cases evolve from patients with latent tuberculosis infection (LTBI). In approximately 5-10% of patients, LTBI progresses to active TB during their lifetime. The number of artificial arthroplasty procedures performed is increasing. The vast majority of people undergoing arthroplasty are aged 60 years and older. Aging and surgical trauma can reduce the ability of the body to fight infection, which can also promote the recurrence of old or dormant TB infections. TB has been reported to reoccur in LTBI patients after arthroplasty who do not receive anti-TB treatment.This article reports the case of an elderly female patient with LTBI and knee osteoarthritis who underwent total knee arthroplasty and achieved good clinical results with anti-TB drug treatment. There is a lack of guidelines for the treatment of patients with LTBI undergoing artificial arthroplasty. This article attempts to provide a time-based treatment approach to reduce the recurrence of LTBI based on a literature review.Case Description: Based on a detailed history, a physical examination, and ancillary examinations, this 71-year-old female patient was found to have no active TB; however, after a positive ɣ-interferon release assay (IGRA) for TB infection, she was diagnosed with LTBI. She underwent artificial knee arthroplasty to treat osteoarthritis of the right knee. Anti-TB drugs were administered 2 weeks after the surgery, and good clinical results were achieved at the 53-month post-operative follow-up with no recurrence of TB.Conclusions: Patients with LTBI who undergo artificial arthroplasty require anti-TB treatment to reduce the risk of TB recurrence.