Sobre um processo de difusão com reinícios não-estáticos sujeito a um campo potencial variante com o tempo

Telles Timóteo da Silva

doi:10.22481/intermaths.v5i1.14959

Autores

Telles Timóteo da Silva Universidade Federal de Juiz de Fora, Ouro Branco - MG, Brasil https://orcid.org/0000-0002-3810-8688

DOI:

https://doi.org/10.22481/intermaths.v5i1.14959

Palavras-chave:

Movimento Browniano num Campo Potencial, Reinício Estocástico, Auto-correlação, Custo Quadrático, Tempo de Primeira Passagem

Resumo

Consideramos uma única partícula difusiva que sofre reinícios não-estáticos, i.e. variantes no tempo, e está imersa num campo potencial também variante no tempo, sob a hipótese de que os reinícios não afetam o potencial. Exibimos alguns resultados novos referentes a momentos e auto-correlação do processo. Observamos que o processo mantém uma correlação sempre positiva entre passado e futuro. Ademais, discutimos sobre uma medida do custo envolvido para reiniciar o processo até que o mesmo atinja um objetivo definido. Além disso, ilustramos o comportamento do processo em exemplos elucidados tanto analiticamente quanto por meio de simulações computacionais, verificando a importância da relação entre a forma funcional do potencial e da função de reinício. Em particular, notamos nos exemplos simulados que a existência do campo potencial pode impedir o processo de atingir um objetivo, mesmo que haja reinício.

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