Time-inhomogeneous diffusions corresponding to symmetric divergence form operators

• Autorzy: Rozkosz A.
• Języki publikacji: EN

Abstrakty

EN

We consider a time-inhomogeneous Markov family (X, P_3,x) corresponding to a symmetric uniformly elliptic divergence form operator. We show that for any φ in the Sobolev space W¹_p∩W¹₂ with p = 2 if d = 1 and p > d > if d > 1 the additive functional X^φ = (φ (X₁)- φ (X_x); 0 ≤ s < t} admits a unique strict decomposition into a martingale additive functional of finite energy and a continuous additive functional of zero energy. Moreover, we give a stochastic representation of the zero energy part and show that in case the diffusion coefficient is regular in time the functional X^φ is a Dirichlet process for each starting point (s, x). The paper contains also rectifications of incorrectly presented or incorrectly proved statements of our earlier paper [14].

Słowa kluczowe

EN

divergence formoperator; Markov family; martingale additive; diffusion coefficient

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 2
• Strony: 231--252
• Opis fizyczny: Biblogr. 20 poz.

Twórcy

autor

Rozkosz A.

• Faculty of Mathematics and Computer Science, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

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