REPRESENTATION OF PATHWISE STATIONARY SOLUTIONS OF STOCHASTIC BURGERS' EQUATIONS
2009 ◽
Vol 09
(04)
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pp. 613-634
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Keyword(s):
In this paper, we show that the stationary solution u(t, ω) of the differentiable random dynamical system U: ℝ+ × L2[0, 1] × Ω → L2[0, 1] generated by the stochastic Burgers' equation with large viscosity, denoted by ν, driven by a Brownian motion in L2[0, 1], is given by: u(t, ω) = U(t, Y(ω), ω) = Y(θ(t, ω)), where Y(ω) can be represented by the following integral equation: [Formula: see text] Here θ is the group of P-preserving ergodic transformations on the canonical probability space [Formula: see text] such that θ(t, ω)(s) = W(t + s) - W(t), where W is the L2[0, 1]-valued Brownian motion on the probability space [Formula: see text], Tν is the linear operator semigroup on L2[0, 1] generated by νΔ.
2010 ◽
Vol 20
(09)
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pp. 2761-2782
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2021 ◽
Vol 382
(2)
◽
pp. 875-949
2010 ◽
Vol 371
(1)
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pp. 210-222
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Keyword(s):
2003 ◽
Vol 2003
(43)
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pp. 2735-2746
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2011 ◽
Vol 11
(02n03)
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pp. 369-388
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1994 ◽
Vol 1
(4)
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pp. 389-402
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