scholarly journals White noise approach to the Itô formula for the stochastic heat equation

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
Alberto Lanconelli
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Stochastic Heat Equation ◽  
Itô Formula ◽  
Ito Formula ◽  
The Stochastic Heat Equation

A REMARK ON THE RENORMALIZED SQUARE OF THE SOLUTION OF THE STOCHASTIC HEAT EQUATION AND ON ITS ASSOCIATED EVOLUTION

2009 ◽  
Vol 12 (03) ◽  
pp. 497-502 ◽  
Author(s):  
ALBERTO LANCONELLI
Keyword(s):  
Heat Equation ◽  
Unbounded Operator ◽  
Chain Rule ◽  
Stochastic Heat Equation ◽  
Itô Formula ◽  
Simple Application ◽  
Second Quantization ◽  
Ito Formula ◽  
The Stochastic Heat Equation

We consider the renormalized square of the solution of the stochastic heat equation and obtain for this process a new dynamic involving the second quantization of an unbounded operator. This is achieved by a version of the Itô formula which we derive by a simple application of the Wick chain rule.

scholarly journals A generalization of the Itô formula

2002 ◽  
Vol 31 (8) ◽  
pp. 477-496
Author(s):  
Said Ngobi
Keyword(s):  
Sobolev Space ◽  
White Noise ◽  
Itô Formula ◽  
Ito Formula ◽  
Integrable Functions ◽  
Square Integrable Functions ◽  
White Noise Space

The classical Itô formula is generalized to some anticipating processes. The processes we consider are in a Sobolev space which is a subset of the space of square integrable functions over a white noise space. The proof of the result uses white noise techniques.

scholarly journals Spatial Moduli of Non-Differentiability for Linearized Kuramoto–Sivashinsky SPDEs and Their Gradient

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1251
Author(s):  
Wensheng Wang
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Fourth Order ◽  
Gaussian Processes ◽  
Three Dimensional ◽  
Space Time ◽  
Symmetry Analysis ◽  
Stochastic Heat Equation ◽  
Moduli Of Continuity

We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto–Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces. We use the underlying explicit kernels and symmetry analysis, yielding spatial moduli of non-differentiability for L-KS SPDEs and their gradient. This work builds on the recent works on delicate analysis of regularities of general Gaussian processes and stochastic heat equation driven by space-time white noise. Moreover, it builds on and complements Allouba and Xiao’s earlier works on spatial uniform and local moduli of continuity of L-KS SPDEs and their gradient.

scholarly journals Dynkin’s Isomorphism Theorem and the Stochastic Heat Equation

2010 ◽  
Vol 34 (3) ◽  
pp. 243-260
Author(s):  
Nathalie Eisenbaum ◽  
Mohammud Foondun ◽  
Davar Khoshnevisan
Keyword(s):  
Heat Equation ◽  
Stochastic Heat Equation ◽  
Isomorphism Theorem ◽  
The Stochastic Heat Equation

scholarly journals Initial measures for the stochastic heat equation

2014 ◽  
Vol 50 (1) ◽  
pp. 136-153 ◽  
Author(s):  
Daniel Conus ◽  
Mathew Joseph ◽  
Davar Khoshnevisan ◽  
Shang-Yuan Shiu
Keyword(s):  
Heat Equation ◽  
Stochastic Heat Equation ◽  
The Stochastic Heat Equation
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