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作者：Porod, U
摘要：For many random walks on ''sufficiently large'' finite groups the so-called cut-off phenomenon occurs: roughly stated, there exists a number k(0), depending on the size of the group, such that it, steps are necessary and sufficient for the random walk to closely approximate uniformity. As a first example on a continuous group, Rosenthal recently proved the occurrence of this cut-off phenomenon for a specific random walk on SO(N). Here we present and [for the case of O(N)] prove results for ran...
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作者：Chen, ZQ; Zhao, Z
作者单位：University of Missouri System; University of Missouri Columbia
摘要：The existence and uniqueness theorem is proved for solutions of the Dirichlet boundary value problems for weakly coupled elliptic systems on bounded domains. The elliptic systems are only assumed to have measurable coefficients and have singular coefficients for the lower-order terms. A probabilistic representation theorem for solutions of the Dirichlet boundary value problems is obtained by using the switched diffusion process associated with the system A strong positivity result for solution...
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作者：Sheu, YC
摘要：We consider the exit measures of (L, alpha)-superdiffusions, 1 < alpha less than or equal to 2, from a bounded smooth domain D in R(d). By using analytic results about solutions of the corresponding boundary value problem, we study the states of the exit measures. (Abraham and Le Gall investigated earlier this problem for a special case L = Delta and alpha = 2.) Also as an application of these analytic results, we give a different proof for the critical Hausdorff dimension of boundary polarity...
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作者：Lalley, SP
摘要：A class of models for riffle shuffles (''f-shuffles'') related to certain expansive mappings of the unit interval is studied. The main result concerns the cycle structure of the resulting random permutations in l(n) when n is large. It describes the asymptotic distribution of the number of cycles of a given length, relating this distribution to dynamical properties of the associated mapping. This result generalizes a recent result of Diaconis, McGrath and Pitman.
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作者：Qian, ZM
摘要：It is known that any smooth, nondegenerate, second-order elliptic operator on a manifold (dimension not equal 2) has the form Delta + B, where B is a vector field and Delta is the Laplace-Beltrami operator under some Riemannian metric on the manifold. In this paper we give several conditions on the ''Ricci curvature'' Ric - del(B)(8) associated with the operator Delta + B to ensure that the diffusion semigroup generated by Delta + B conserves probability and possesses the Feller property.
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作者：Mueller, C
摘要：We consider the equation u(t) = u(xx) + u(gamma)W, t > 0, 0 less than or equal to x less than or equal to J, u(0,x) = u(0)(x), u(t,0) = u(t,J) = 0, where W = W(t,x) is two-parameter white noise. We show local existence and uniqueness for unbounded initial conditions satisfying certain conditions. Our results are motivated by earlier work, which showed that, for large gamma, solutions of this equation can blow up. One would wish to show that solutions can be extended beyond blowup, and our resu...
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作者：Kallenberg, O
摘要：Assume that weak existence and pathwise uniqueness hold for solutions to the equation dX(t) = sigma(t, X) dB(t) + b(t, X) dt starting at fixed points. Then there exists a Borel measurable function F, such that any solution (X, B) satisfies X = F(X(0), B) a.s. This strengthens a fundamental result of Yamada and Watanabe, where F may depend on the initial distribution mu.
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作者：Marton, K; Shields, PC
作者单位：University System of Ohio; University of Toledo
摘要：Jeff Steif has brought to our attention an error on page 975 of our paper. Our argument that inequality (30) implies the immediately following inequality has a gap. A closer look shows an even more serious problem, namely, Lemma 6 as stated is probably not true, since nothing in the weak Bernoulli property precludes the possibility that splitting sets for x(1)(n) may depend on past coordinates {x(1): i less than or equal to 0}. With a modified definition of the splitting concept an alternative...
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作者：Mountford, TS; Port, SC
摘要：We examine the structure of the range of a stable process with drift near its initial position and derive an integral test to determine the rate of growth of the size of intervals in the complement of the range. This integral test depends on the random number of excursions that the process makes away from the initial point.
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作者：Dalang, RC; Mountford, T
作者单位：University of California System; University of California Los Angeles
摘要：For a Brownian sheet on the nonnegative quadrant, we show that any nontrivial curve in the quadrant with the property that the Brownian sheet restricted to the curve gives rise to a differentiable function cannot be differentiable at any point. This result has several implications for level sets of the Brownian sheet. In particular, any Jordan are contained in a level set must be nowhere differentiable.
