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作者：Fuhrman, M; Tessitore, G
作者单位：Polytechnic University of Milan; University of Parma
摘要：Solutions of semilinear elliptic differential equations in infinite-dimensional spaces are obtained by means of forward and backward infinite-dimensional stochastic evolution equations. The backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition. Elliptic equations are intended in a mild sense, suitable also for applications to optimal control. We finally notice that, due to the lack of smoothing properties, the elliptic partial ...
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作者：Ball, F; Neal, P
作者单位：University of Nottingham; Lancaster University
摘要：This paper is concerned with a stochastic model for the spread of an epidemic among a population of n individuals, labeled 1, 2,. .., n, in which a typical infected individual, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently according to the contact distribution V-i(n) = {nu(i, j,)(n) ; j = 1, 2,. . . n}, at the points of independent Poisson processes with rates gimel(G)(n) an...
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作者：Bank, P; El Karoui, N
作者单位：Humboldt University of Berlin; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：We study a new type of representation problem for optional processes with connections to singular control, optimal stopping and dynamic allocation problems. As an application, we show how to solve a variant of Skorohod's obstacle problem in the context of backward stochastic differential equations.
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作者：Dembo, A; Gantert, N; Zeitouni, O
作者单位：Stanford University; Stanford University; Technion Israel Institute of Technology; Technion Israel Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities; Helmholtz Association; Karlsruhe Institute of Technology
摘要：Suppose that the integers are assigned the random variables {w(x), mu(x)} (taking values in the unit interval times the space of probability measures on R+), which serve as an environment. This environment defines a random walk {X-t} (called a RWREH) which, when at x, waits a random time distributed according to mu(x) and then, after one unit of time, moves one step to the right with probability omega(x), and one step to the left with probability 1 - omega(x). We prove large deviation principl...
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作者：Lutwak, E; Yang, D; Zhang, GY
作者单位：New York University; New York University Tandon School of Engineering
摘要：It is shown that the product of the Renyi entropies of two independent random vectors provides a sharp lower bound for the expected value of the moments of the inner product of the random vectors. This new inequality contains important geometry (such as extensions of one of the fundamental affine isoperimetric inequalities, the Blaschke-Santalo inequality).
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作者：Burdzy, K; Chen, ZQ; Sylvester, J
作者单位：University of Washington; University of Washington Seattle
摘要：The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as noncylindrical domains, and its connections with partial differential equations. Construction is given for RBM in C-3-smooth time-dependent domains in the n-dimensional Euclidean space R-n. We present various sample path properties of the process, two-sided estimates for its transition density function, and a probabilistic representation of solutions to some partial diffe...
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作者：Diaconis, P; Mayer-Wolf, E; Zeitouni, O; Zerner, MPW
作者单位：Stanford University; Stanford University; University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider a Markov chain on the space of (countable) partitions of the interval [0, 1], obtained first by size-biased sampling twice (allowing repetitions) and then merging the parts (if the sampled parts are distinct) or splitting the part uniformly (if the same part was sampled twice). We prove a conjecture of Vershik stating that the Poisson-Dirichlet law with parameter theta = 1 is the unique invariant distribution for this Markov chain. Our proof uses a combination of probabilistic, com...
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作者：Comets, F; Zeitouni, O
作者单位：Universite Paris Cite; University of Minnesota System; University of Minnesota Twin Cities
摘要：We prove a law of large numbers for a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a weak mixing field in the sense of Dobrushin and Shlosman. Our result holds if the mixing rate balances moments of some random times depending on the path. It applies in the nonnestling case, but we also provide examples of nestling walks that satisfy our assumptions. The derivation is b...
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作者：Becker-Kern, P; Meerschaert, MM; Scheffler, HP
作者单位：Dortmund University of Technology; Nevada System of Higher Education (NSHE); University of Nevada Reno
摘要：Scaling limits of continuous time random walks are used in physics to model anomalous diffusion, in which a cloud of particles spreads at a different rate than the classical Brownian motion. Governing equations for these limit processes generalize the classical diffusion equation. In this article, we characterize scaling limits in the case where the particle jump sizes and the waiting time between jumps are dependent. This leads to an efficient method of computing the limit, and a surprising c...
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作者：Bernardin, C
作者单位：Universite Paris Saclay
摘要：We consider the simple asymmetric exclusion process with nonzero drift under the stationary Bernoulli product measure at density rho. We prove that for dimension d = 2 the occupation time of the site 0 is diffusive as soon as rho not equal 1/2. For dimension d = 1, if the density rho is equal to 1/2, we prove that the time t variance of the occupation time of the site 0 diverges in a certain sense at least as t(5/4).
