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作者：Baudoin, F; Thieullen, M
作者单位：Technische Universitat Wien; Universite Paris Cite; Sorbonne Universite
摘要：For a given functional Y on the path space, we define the pinning class of the Wiener measure as the class of probabilities which admit the same conditioning given Y as the Wiener measure. Using stochastic analysis and the theory of initial enlargement of filtration, we study the transformations (not necessarily adapted) which preserve this class. We prove, in this non Markov setting, a stochastic Newton equation and a stochastic Noether theorem. We conclude the paper with some non canonical r...
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作者：Dawson, DA; Li, ZH
作者单位：Carleton University; Beijing Normal University
摘要：A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional excursions.
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作者：Donati-Martin, C
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We develop a stochastic integration with respect to a q-Brownian motion (for -1 < q < 1), i.e. a non commutative process X, = a, + a(t)* where the operator at and its adjoint fulfill the q commutation relation a(s)a(t)* - qa(t)*a(s) = (S boolean AND t) 1; under the vacuum state expectation. We show that this process enjoys a predictable representation type property.
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作者：Uzun, HB; Alexander, KS
作者单位：University of Southern California
摘要：We consider boundary roughness for the droplet created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l(2), for large l. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large l this maximum is at least of order l(1/3) (log l)(-2/3). This complements the upper bound of order l(1/3) (log l)(2/3) ...
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作者：Bogdan, K; Burdzy, K; Chen, ZQ
作者单位：Wroclaw University of Science & Technology; University of Washington; University of Washington Seattle
摘要：We present several constructions of a censored stable process in an open set D subset of R, i.e., a symmetric stable process which is not allowed to jump outside D. We address the question of whether the process will approach the boundary of D in a finite time - we give sharp conditions for such approach in terms of the stability index alpha and the thickness of the boundary. As a corollary, new results are obtained concerning Besov spaces on non-smooth domains, including the critical exponent...
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作者：Li, XD
作者单位：University of Oxford
摘要：We introduce Sobolev spaces and capacities on the path space P-m0 (M) over a compact Riemannian manifold M. We prove the smoothness of the Ito map and the stochastic anti-development map in the sense of stochastic calculus of variation. We establish a Sobolev norm comparison theorem and a capacity comparison theorem between the Wiener space and the path space P-m0 (M). Moreover, we prove the tightness of (r, p)-capacities on P-m0 (M), r is an element of N, p > 1, which generalises a result due...
