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- Stochastic_partial_differential_equation abstract "Stochastic partial differential equations (SPDEs) are similar to ordinary stochastic differential equations. They are essentially partial differential equations that have random forcing terms and coefficients. They can be exceedingly difficult to solve. However, they have strong connections with quantum field theory and statistical mechanics.One difficulty encountered when dealing with stochastic PDEs is their lack of regularity. For example, one of the most classical SPDEsis given by the stochastic heat equation which can formally be written aswhere denotes space-time white noise and is the Laplacian.In one space dimension, solutions to this equation are only almost 1/2-Hölder continuous in space and 1/4-Hölder continuous in time.For dimensions two and higher, solutions are not even function-valued, but can be made sense of as random distributions.".
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- Stochastic_partial_differential_equation wikiPageRevisionID "562568418".
- Stochastic_partial_differential_equation hasPhotoCollection Stochastic_partial_differential_equation.
- Stochastic_partial_differential_equation subject Category:Partial_differential_equations.
- Stochastic_partial_differential_equation subject Category:Stochastic_differential_equations.
- Stochastic_partial_differential_equation type Abstraction100002137.
- Stochastic_partial_differential_equation type Communication100033020.
- Stochastic_partial_differential_equation type DifferentialEquation106670521.
- Stochastic_partial_differential_equation type Equation106669864.
- Stochastic_partial_differential_equation type MathematicalStatement106732169.
- Stochastic_partial_differential_equation type Message106598915.
- Stochastic_partial_differential_equation type PartialDifferentialEquation106670866.
- Stochastic_partial_differential_equation type PartialDifferentialEquations.
- Stochastic_partial_differential_equation type Statement106722453.
- Stochastic_partial_differential_equation type StochasticDifferentialEquations.
- Stochastic_partial_differential_equation comment "Stochastic partial differential equations (SPDEs) are similar to ordinary stochastic differential equations. They are essentially partial differential equations that have random forcing terms and coefficients. They can be exceedingly difficult to solve. However, they have strong connections with quantum field theory and statistical mechanics.One difficulty encountered when dealing with stochastic PDEs is their lack of regularity.".
- Stochastic_partial_differential_equation label "Stochastic partial differential equation".
- Stochastic_partial_differential_equation sameAs m.02w7sdy.
- Stochastic_partial_differential_equation sameAs Q16979017.
- Stochastic_partial_differential_equation sameAs Q16979017.
- Stochastic_partial_differential_equation sameAs Stochastic_partial_differential_equation.
- Stochastic_partial_differential_equation wasDerivedFrom Stochastic_partial_differential_equation?oldid=562568418.
- Stochastic_partial_differential_equation isPrimaryTopicOf Stochastic_partial_differential_equation.