Personas are a particularly useful testing tool for storytelling robots for people with dementia (PwD) because they offer an alternative to direct user involvement, which is often limited by recruitment, privacy, and consent-related challenges. The manual creation of realistic personas is often complex and time-intensive, whereas pretrained large language models (LLMs) offer a promising alternative due to their impressive zero-shot and in-context role-playing performance. This study investigates whether commercially available LLMs can accurately simulate personas of PwD for use in testing of a storytelling robot for PwD. To this end, we developed a custom probabilistic system based on a single prompt chain composed of multiple few-shot and zero-shot prompts, along with an independent storage system for custom memory manipulation. The simulated personas underwent repeated assessments using the Mini-Mental State Examination (MMSE), a standardized assessment for evaluating memory, comprehension, and executive function. Results demonstrated statistical similarity to real scores and indicated that LLM-based personas can closely mirror many of the cognitive profiles characteristic of these conditions: early-stage Alzheimer's personas exhibited marked impairments in recent memory, late-stage Alzheimer's personas showed significant global cognitive impairment, and vascular dementia personas displayed relatively preserved memory but reduced executive functioning. These findings indicate that pretrained LLMs possess the capability to simulate accurate personas of PwD to a significant extent.