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作者：Artstein, Z
作者单位：Weizmann Institute of Science; Universite de Montpellier
摘要：The collection of sub-sigma -fields of a Borel measure space when endowed with the topology of strong convergence is in general not a compact space. The paper offers a completion of this space which makes it compact. The elements which are added to the space are called relaxed sigma -fields. A notion of relaxed conditional expectation with respect to it relaxed sigma -field is identified. The relaxed conditional expectation is a probability measure-valued map. It is shown that the conditional ...
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作者：Bernabei, MS
作者单位：University of Camerino
摘要：The Central Limit Theorem for a model of discrete-time random walks on the lattice Z(nu) in a fluctuating random environment was proved for almost-all realizations of the space-time environment, for all nu > 1 in [BMP1] and for all nu greater than or equal to 1 in [BBMP]. in [BMP1] it was proved that the random correction to the average of the random walk for nu greater than or equal to 3 is finite. In the present paper we consider the cases nu = 1, 2 and prove the Central Limit Theorem as T -...
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作者：Bass, RF; Chen, ZQ
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：We consider the stochastic differential equation dX(t) = a(X-t)dW(t) + b(X-t)dt, where W is a one-dimensional Brownian motion. We formulate the notion of solution and prove strong existence and pathwise uniqueness results when a is in C-1/2 and b is only a generalized function, for example, the distributional derivative of a Holder function or of a function of bounded variation. When b = aa', that is, when the generator of the SDE is the divergence form operator L = 1/2 d/dx (a(2) d/dx), a res...
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作者：Delmas, JF; Fleischmann, K
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Consider the catalytic super-Brownian motion X-rho (reactant) in R-d, d less than or equal to 3, which branching rates vary randomly in time and space and in fact are given by an ordinary super-Brownian motion rho (catalyst). Our main object of study is the collision local time L = L-[rho ,L-Xo](d(s, x)) of catalyst and reactant. It determines the covariance measure in the martingale problem for X-rho and reflects the occurrence of hot spots of reactant which can be seen in simulations of X-rh...
