Recent developments on stochastic heat equation with additive fractional-colored noise

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Ciprian Tudor
Keyword(s):  
Comparative Study ◽  
Heat Equation ◽  
Gaussian Noise ◽  
Colored Noise ◽  
Covariance Structure ◽  
Stochastic Heat Equation ◽  
Basic Properties ◽  
Recent Developments

AbstractWe expose some recent and less recent results related to the existence and the basic properties of the solution to the linear stochastic heat equation with additive Gaussian noise. We will make a comparative study of the behavior of the solution in function of the covariance structure of the driving noise.

scholarly journals On the law of the solution to a stochastic heat equation with fractional noise in time

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Solesne Bourguin ◽  
Ciprian A. Tudor
Keyword(s):  
Brownian Motion ◽  
Heat Equation ◽  
Fractional Brownian Motion ◽  
Gaussian Noise ◽  
Stochastic Heat Equation ◽  
Bifractional Brownian Motion ◽  
Fractional Noise ◽  
The Stochastic Heat Equation ◽  
The Law

AbstractWe study the law of the solution to the stochastic heat equation with additive Gaussian noise which behaves as the fractional Brownian motion in time and is white in space. We prove a decomposition of the solution in terms of the bifractional Brownian motion. Our result is an extension of a result by Swanson.

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