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- W2178233184 abstract "Let M be a connected, smooth, compact manifold of dimension N, and consider the following Stratonovich stochastic differential equation on M 1.1 $$ left{ begin{gathered} dxi _t left( x right) = sumlimits_{k = 1}^d {X_k left( {xi _t left( x right)} right) circ dW_t^k + X_0 left( {xi _t left( x right)} right)dt} hfill xi _0 left( x right) = x. hfill end{gathered} right. $$ Here X 0, X 1,...X d are smooth vector fields on M and {W : t ≥ 0}, 1 ≤ k ≤ d, are independent real valued Brownian motions on some probability space (Ώ, F, ℙ). For each x ∈ M (1.1) has a (unique) strong solution which is a diffusion on M with generator 1.2 $$ L = tfrac{1} {2}sumlimits_{k = 1}^d {X_k^2 + X_0 } . $$" @default.
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- W2178233184 date "1991-01-01" @default.
- W2178233184 modified "2023-09-23" @default.
- W2178233184 title "Statistical Equilibrium and Two-Point Motion for a Stochastic Flow of Diffeomorphisms" @default.
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