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作者：Lee, TY; Remillard, B
作者单位：University of Quebec; University of Quebec Trois Rivieres
摘要：Let mu(t)(dx) denote a three-dimensional super-Brownian motion with deterministic initial state mu(0)(dx) = dx, the Lebesgue measure. Let V: R(3) --> R be Holder-continuous with compact support, not identically zero and such that integral(R3)V(x) dx = 0. We show that log P {integral(0)(t) integral(R3)V(x)mu(s)(dx)ds > bt(3/4)} is of order t(1/2) as t --> infinity, for b > 0. This should be compared with the known result for the case integral(R3)V(x)dx > 0. In that case the normalization bt(3/4...
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作者：Sudbury, A; Lloyd, P
摘要：Duality has proved to be a powerful tool in the theory of interacting particle systems. The approach in this paper is algebraic rather than via Harris diagrams. A form of duality is found which includes coalescing and annihilating duality as special cases. This enables new results for the branching annihilating random walk and the biased annihilating branching process to be derived.
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作者：Pinsky, RG
摘要：Consider the supercritical super-Brownian motion X(t, .) on R(d) corresponding to the evolution equation u(t) = D/2 Delta u + u - u(2). We obtain rather tight bounds on P-mu(X(s, B-n(c)(0)) = 0, for all s is an element of [0, t]) and on P-mu(X(t, B-n(c)(0)) = 0), for large n, where P-mu denotes the measure corresponding to the supercritical super-Brownian motion starting from the finite measure, mu, B-n(0) subset of R(d) denotes the ball of radius n centered at the origin and B-n(c)(0) denotes...
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作者：Stong, R
摘要：In this paper we discuss and apply a novel method for bounding the eigenvalues of a random walk on a group G (or equivalently on its Cayley graph). This method works by looking at the action of an Abelian normal subgroup H of G on G. We may then choose eigenvectors which fall into representations of H. One is then left with a large number (one for each representation of H) of easier problems to analyze. This analysis is carried out by new geometric methods. This method allows us to give bounds...
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作者：Sowers, RB
作者单位：University of Southern California
摘要：In this paper we prove some intermittency-type estimates for the stochastic partial differential equation du = L u dt + M(1)u circle dW(t)(l), where L is a strongly elliptic second-order partial differential operator and the M(l)'s are first-order partial differential operators. Here the W-l's are standard Wiener processes and circle denotes Stratonovich integration. We assume for simplicity that u(0, .) equivalent to 1. Our interest here is the behavior of E[\ u(t, x)\(p)] for large time and ...
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作者：Grimmett, G
摘要：The random-cluster model is a generalization of percolation and ferromagnetic Potts models, due to Fortuin and Kasteleyn. Not only is the random-cluster model a worthwhile topic for study in its own right, but also it provides much information about phase transitions in the associated physical models. This paper serves two functions. First, we introduce and survey random-cluster measures from the probabilist's point of view, giving clear statements of some of the many open problems. Second, we...
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作者：Vanderbei, RJ
摘要：Let D be a compact, convex domain in d-dimensional Euclidean space and let f be a nonnegative real-valued function defined on D. The classical optimal stopping problem is to find a stopping time tau* that attains the supremum v(x) = sup(tau) E(x)f(B(tau)). Here, B is a d-dimensional Brownian motion with absorption on the boundary of D and the supremum is over all stopping times. It is well known that v is characterized as the smallest superharmonic majorant of f. In this paper, we modify this ...
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作者：Baldi, P
摘要：We study the asymptotics of the exit probability P-x, s(epsilon){tau less than or equal to T), where tau is the exit time from an open set and P-x, s(epsilon), is the law of a diffusion process with a small parameter epsilon multiplying the diffusion coefficient. We consider the case of the Brownian bridge in many dimensions, this choice being motivated by applications to numerical simulation. The method uses recent results reducing the problem to the solution of a system of linear first-order...
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作者：Cairoli, R; Dalang, RC
作者单位：Tufts University
摘要：This paper is motivated by remarkable results of Mandelbaum, Shepp and Vanderbei concerning an optimal switching problem for two Brownian motions. In this paper, the discrete form of this problem, in which the Brownian motions are replaced by random walks, is studied and solved without any restriction on the boundary data. The method proposed here involves uncovering the structure of the solution using combinatorial and geometric arguments, and then providing a characterization for the two typ...
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作者：Stong, R
摘要：In this paper we give sharp bounds on the eigenvalues of the natural random walk on the Burnside group B(3, n). Most of the argument uses established geometric techniques for eigenvalue bounds. However, the most interesting bound, the upper bound on the second largest eigenvalue, cannot be done by existing techniques. To give a bound we use a novel method for bounding the eigenvalues of a random walk on a group G (or equivalently its Cayley graph). This method works by choosing eigenvectors wh...
