How does fractional Brownian motion influence stochastic differential equations in Hilbert spaces? This paper explores stochastic differential equations involving cylindrical fractional Brownian motion with a Hurst parameter between 1/2 and 1. Focusing on mild solutions, the research verifies their existence, uniqueness, sample path continuity, and state space regularity, also demonstrating the existence of limiting measures. Furthermore, the paper confirms the probability law equivalence for solutions at different times and initial conditions, along with the convergence of these probability laws towards a limiting probability. These theoretical results are then applied to stochastic parabolic and hyperbolic differential equations. The findings offer insights into the behavior of stochastic systems influenced by fractional Brownian motion.
This theoretical study, published in Stochastics and Dynamics, aligns with the journal's focus on stochastic processes and their applications. By investigating fractional Brownian motion in Hilbert spaces, the paper contributes to the journal's coverage of advanced mathematical tools used to model complex dynamical systems.
| Category | Category Repetition |
|---|---|
| Technology: Engineering (General). Civil engineering (General) | 1 |
| Science: Mathematics | 1 |