Note on abstract stochastic semilinear evolution equations

2015/08/28 by Ta, Ton Viet · 3 citations
#35R60 #58D25 #60H15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1508.07211

Abstract

This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular dependence of the solutions on initial data. Finally, some applications to stochastic partial differential equations are presented.

Cited by

• Modeling Predator-Prey Dynamics with Stochastic Differential Equations: Patterns of Collective Hunting and Nonlinear Predation Effects
• Towards High-Fidelity and Controllable Bioacoustic Generation via Enhanced Diffusion Learning
• Deep Learning for Automated Identification of Vietnamese Timber Species: A Tool for Ecological Monitoring and Conservation

Related

• A note on stochastic semilinear dissipative evolution equations
• Abstract stochastic evolution equations in M-type 2 Banach spaces
• Stochastic parabolic evolution equations in M-type 2 Banach spaces
• On well-posedness of semilinear stochastic evolution equations on L_p spaces
• Well-posedness for a class of dissipative stochastic evolution equations with Wiener and Poisson noise