A note on stochastic semilinear dissipative evolution equations

2025/12/20 by Carlo Marinelli, Marinelli, Carlo
Economics, Econometrics and Finance · Engineering · Mathematics · #Stochastic processes and financial applications #Stability and Controllability of Differential Equations #Nonlinear Differential Equations Analysis

paper · doi:10.48550/arxiv.2512.18398

Abstract

Existence and uniqueness of mild solutions to a class of semilinear stochastic evolution equations with additive noise is proved. The linear part of the drift term is the generator of a compact semigroup of contractions, while the nonlinear part is only assumed to be the superposition operator associated to a decreasing function.

Citations

• Well-posedness of monotone semilinear SPDEs with semimartingale noise

Related

• Well-posedness for a class of dissipative stochastic evolution equations with Wiener and Poisson noise
• On uniqueness of mild solutions for dissipative stochastic evolution equations
• Note on abstract stochastic semilinear evolution equations
• On mild solutions to some dissipative SPDEs on L^p spaces with additive noise
• Stochastic Evolution Equations with Multiplicative Poisson Noise and Monotone Nonlinearity: A New Approach