-
作者：Dalang, RC; Mountford, T
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of California System; University of California Los Angeles
摘要：Distinct excursion intervals of a Brownian motion (that correspond to a fixed level) have no common endpoints. What is the situation for distinct excursion sets of a Brownian sheet? These sets are termed Brownian bubbles in the literature, and this paper examines how bubbles from fixed or random levels come into contact with each other, by examining whether or not the Brownian sheet restricted to a specific type of curve can have a point of increase. At random levels, we show that points of in...
-
作者：Winkel, M
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：We analyze the existence and properties of right inverses K for nonsymmetric Levy processes X, extending recent work of Evans 171 in the symmetric setting. First, both X and -X have right inverses if and only if X is recurrent and has a nontrivial Gaussian component, Our main result is then a description of the excursion measure n(Z) of the strong Markov process Z = X - L (reflected process) where L-t = inf{x > 0 : K-x > t}. Specifically, n(Z) is essentially the restriction of n(X) to the excu...
-
作者：Bossy, M; Jourdain, B
作者单位：Inria; Institut Polytechnique de Paris; Ecole des Ponts ParisTech
摘要：In this paper, we give a probabilistic interpretation of a viscous scalar conservation law in a bounded interval thanks to a nonlinear martingale problem. The underlying nonlinear stochastic process is reflected at the boundary to take into account the Dirichlet conditions. After proving uniqueness for the martingale problem, we show existence thanks to a propagation of chaos result. Indeed we exhibit a system of N interacting particles, the empirical measure of which converges to the unique s...
-
作者：Buckdahn, R; Ma, J
作者单位：Universite de Bretagne Occidentale; Purdue University System; Purdue University
摘要：In this paper we study a new type of Taylor expansion for Ito-type random fields, up to the second order. We show that an M-type random field with reasonably regular integrands can be expanded, up to the second order, to the linear combination of increments of temporal and spatial variables, as well as the driven Brownian motion, around even a random (t, x)-point. Also, the remainder can be estimated in a pathwise manner. We then show that such a Taylor expansion is valid for the solutions to ...
-
作者：Borisov, IS; Ruzankin, PS
作者单位：Russian Academy of Sciences; Sobolev Institute of Mathematics
摘要：Under minimal moment conditions complete asymptotic. expansions are obtained for expectations of unbounded functions of a finite family of independent random variables in the Poissonian setting when the distributions of the random variables have large atoms at zero.
-
作者：Jiang, TF
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Let {X-i; i greater than or equal to 1}, {Y-i; i > 1}, {U, U-i; i > 1} and {V, V-i; i greater than or equal to 1} be four i.i.d. sequences of random variables. Suppose U and V are uniformly distributed on [0, 1](3). For each realization of {U-j; 1 less than or equal to j less than or equal to n}, {X-i,X-p; 1 less than or equal to p less than or equal to n} is constructed as a certain permutation of {X-p; 1 less than or equal to p less than or equal to n} for any 1 less than or equal to i less ...
-
作者：König, W; Mörters, P
作者单位：Technical University of Berlin; University of Bath
摘要：We equip the intersection of p independent Brownian paths in R-d, d greater than or equal to 2, with the natural measure l defined by projecting the intersection local time measure via one of the Brownian motions onto the set of intersection points. Given a bounded domain U subset of R-d we show that, as a up arrow infinity, the probability of the event {l(U) > a} decays with an exponential rate of a(1)/ptheta, where theta is described in terms of a variational problem. In the important specia...
-
作者：Griffin, PS; Qazi, FS
作者单位：Syracuse University; St. Marys College of Maryland
摘要：Let X, X-1, X-2,... be a sequence of independent and identically distributed random variables. Let X-(1)(n),...,X-(n)(n) be an arrangement of X-1, X-2,..., X-n in decreasing order of magnitude, and set((rn))S(n) = X-(rn+1)(n) + (...) + X-(n)(n). This is known as the modulus trimmed sum. We obtain a complete characterization of the class of limit laws of the normalized modulus trimmed sum when the underlying distribution is symmetric and r(n) --> infinity, r(n)n(-1) --> 0.
-
作者：Engländer, L; Turaev, D
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Consider the or-finite measure-valued diffusion corresponding to the evolution equation u(t) = Lu + beta(x)u - f(x, u), where f(x, u) = alpha(x)u(2) + integral(0)(infinity) (e(-ku) - 1 + ku)n (x, dk) and n is a smooth kernel satisfying an integrability condition. We assume that beta, alpha is an element of C-eta (R-d) with eta is an element of (0, 1), and alpha > 0. Under appropriate spectral theoretical assumptions we prove the existence of the random measure lim(tup arrowinfinity)(e-lambdact...
-
作者：Le Jan, Y; Raimond, O
作者单位：Universite Paris Saclay
摘要：Using the Wiener chaos decomposition, we show that strong solutions of non-Lipschitzian stochastic differential equations are given by random Markovian kernels. The example of Sobolev flows is studied in some detail, exhibiting interesting phase transitions.
