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2013 8 19 8 20 2 (D-301)8 19 14:30 – 16:00 Integrals along rough paths and Lyons’ extension theorem via fractional calculus16:30 – 18:00 On a stability of heat kernel estimates under generalized non-local Feynman-Kacperturbations8 20 10:30 – 12:00 13:30 – 15:00 φ- Wasserstein • .http://www.ems.okayama-u.ac.jp/appl/shiozawa/Okayama-AP-seminar.html

Integrals along rough paths and Lyons’ extension theorem viafractional calculus () fractional calculus 1 fractionalderivative Gubinelli (2002) controlled path Lyons On a stability of heat kernel estimates under generalized non-localFeynman-Kac perturbations ()It is well known that the condition for stability of Feynman-Kac semigroup given by acontinuous additive functional of finite variation can be characterized in analytically.this talk, we consider an analytic characterization for the stability of so-called generalizedFeynman-Kac semigroup given by additive functionals involving all three components: acontinuous part with finite variation, a continuous part of zero energy (not necessarily offinite variation) and a purely discontinuous part.The basic strategy in obtaining our analytic characterization is to apply the results on theanalytic characterization of gaugeability for generalized Feynman-Kac transforms studied inKim-Kuwae (2012), to the methods developed by Takeda (2006, 2007) and Wada (2013).In particular, we will show that the extra assumptions on potentials appeared in Takeda(2006) and Wada (2013) (they should be of positive smooth measures of finite energy integrals)can be removed successfully by using the so-called generalized Fukushima decompositionin the strict sense. (This is a joint work with K. Kuwae).Inφ- Wasserstein ()φ-, Wasserstein. Wasserstein, φ-. , .

∗R d α- (X t , P x ), α < d, (E (α) , D(E (α) )) V :{∫}inf E (α) (u, u) ; u ∈ D(E (α) ), u2 (x)V(x)dx = 1R d > 1. (1)V, W R d R W R (x) = W(x + R), q R (x) = V(x) + W R (x) (2) |R| q R :{∫}β ∞ (q R ) := sup E x [e Aq R ∞] < ∞ ⇐⇒ inf E (α) (u, u) ; u ∈ D(E (α) ), u2 (x)q R (x)dx = 1 > 1, (3)x∈R d R dA q R ∞ = ∫ ∞0 q R(X t )dt. |R| Theorem 1.lim β ∞(q R ) = β ∞ (V) ∨ β ∞ (W). (4)R→∞ B. Simon(1980) α = 2 V W R |R| α−dR Theorem 1 ∗ 1