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作者：Burdzy, K; Le Gall, JF
作者单位：University of Washington; University of Washington Seattle; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider super-Brownian motion whose historical paths reflect from each other. unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results about path behavior for processes under any limit distribution. In particular, we show that for any gamma > 0, a typical increment of a reflecting historical path over a...
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作者：Mörters, P
作者单位：University of Kaiserslautern
摘要：In this paper we investigate fast particles in the range and support of super-Brownian motion in the historical setting. In this setting each particle of super-Brownian motion alive at time t is represented by a path w : [0, t] --> R-d and the state of historical super-Brownian motion is a measure on the set of paths. Typical particles have Brownian paths, however in the uncountable collection of particles in the range of a super-Brownian motion there are some which at exceptional times move f...
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作者：Brown, H; Hobson, D; Rogers, LCG
作者单位：University of Bath
摘要：Let (M-t) be any martingale with M-0 = 0, an intermediate law M-1 similar to mu (1), and terminal law M-2 similar to mu (2), and let (M) over bar (2) = sup(0 less than or equal to1 less than or equal to2) M-t. In this paper we prove that there exists an upper bound, with respect to stochastic ordering of probability measures, on the law of (M) over bar (2). We construct, using excursion theory, a martingale which attains this maximum. Finally we apply this result to the robust hedging of a loo...
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作者：Talagrand, M
作者单位：Sorbonne Universite; University System of Ohio; Ohio State University
摘要：We study the Hopfield model at temperature 1, when the number M(N) of patterns grows a bit slower than N. We reach a good understanding of the model whenever M(N) less than or equal to N/(log N)(11). For example, we show that if M(N) --> infinity, for two typical configurations sigma (1), sigma (2), (Sigma (i less than or equal toN)sigma (1)(i)sigma (2)(i))(2) is close to NM(N).
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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...
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作者：Léandre, R; Mohammed, SEA
作者单位：Universite de Lorraine; Southern Illinois University System; Southern Illinois University
摘要：In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.
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作者：Bogachev, VI; Röckner, M
作者单位：Lomonosov Moscow State University; University of Bielefeld
摘要：We introduce and study a new concept of a weak elliptic equation for measures on infinite dimensional spaces. This concept allows one to consider equations whose coefficients are not globally integrable. By using a suitably extended Lyapunov function technique, we derive a priori estimates for the solutions of such equations and prove new existence results. As an application, we consider stochastic Burgers, reaction-diffusion, and Navier-Stokes equations and investigate the elliptic equations ...
