A Stochastic Parabolic Equation with Nonlinear Flux on the Boundary Driven by a Gaussian Noise

2014 ◽  
Vol 46 (1) ◽  
pp. 780-802 ◽  
Author(s):  
Viorel Barbu ◽  
Stefano Bonaccorsi ◽  
Luciano Tubaro
Keyword(s):  
Parabolic Equation ◽  
Gaussian Noise ◽  
Stochastic Parabolic Equation

scholarly journals Rescaling nonlinear noise for 1D stochastic parabolic equations

2019 ◽  
Vol 20 (04) ◽  
pp. 2050027
Author(s):  
Beniamin Goldys ◽  
Misha Neklyudov
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Space Variable ◽  
Nonlinear Noise ◽  
Stochastic Parabolic Equation

We show regularization effect of nonlinear gradient noise to the solution of 1D stochastic parabolic equation. We demonstrate convergence to a martingale (independent upon space variable) when we rescale noise at the extremum points of the process.

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