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作者：Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation dX(t) = vertical bar X-t vertical bar(alpha) dW(t), where W-t is a one-dimensional Brownian motion and alpha is an element of (0, 1/2). Weak uniqueness does not hold for the solution to this equation. If one restricts attention, however, to those solutions that spend zero time at 0, then pathwise uniqueness does hold and a strong solution exists. We also consider a class...
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作者：Kahn, Jeff; Weininger, Nicholas
摘要：A fractional fuzzy Potts measure is a probability distribution on spin configurations of a finite graph G obtained in two steps: first a subgraph of G is chosen according to a random cluster measure phi(p,q), and then a spin ( 1) is chosen independently for each component of the subgraph and assigned to all vertices of that component. We show that whenever q : 1, such a measure is positively associated, meaning that any two increasing events are positively correlated. This generalizes earlier ...
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作者：Russo, Francesco; Trutnau, Gerald
作者单位：Universite Paris 13; University of Bielefeld
摘要：A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.
