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作者：Slomczynski, W; Zastawniak, T
作者单位：Jagiellonian University; University of Hull
摘要：Expected utility maximization problems in mathematical finance lead to a generalization of the classical definition of entropy. It is demonstrated that a necessary and sufficient condition for the second law of thermodynamics to operate is that any one of the generalized entropies should tend to its minimum value of zero.
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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：Zambotti, L
作者单位：Scuola Normale Superiore di Pisa; University of Bielefeld
摘要：We consider the solution (u, eta) of the white-noise driven stochastic partial differential equation with reflection on the space interval [0, 1] introduced by Nualart and Pardoux, where eta is a reflecting measure on [0, infinity) x (0, 1) which forces the continuous function u, defined on [0, infinity) x [0, 1], to remain nonnegative and eta has support in the set of zeros of u. First, we prove that at any fixed time t > 0, the measure eta([0, t] x dtheta) is absolutely continuous w.r.t. the...
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作者：Aida, S
作者单位：University of Osaka
摘要：We prove weak Poincare inequalities on domains which are inverse images of open sets in Wiener spaces under continuous functions of Brownian rough paths. The result is applicable to Dirichlet forms on loop groups and connected open subsets of path spaces over compact Riemannian manifolds.
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作者：Delarue, F
作者单位：Universite Paris Cite
摘要：We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the theory of forward-backward stochastic differential equations and introduce the new concept of auxiliary SDEs.
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作者：Peccati, G
作者单位：Universite Paris Saclay; Bocconi University
摘要：Consider a (possibly infinite) exchangeable sequence X = {X-n : 1 less than or equal to n < N}, where N is an element of N boolean OR {infinity}, with values in a Borel space (A, A), and note X-n = (X-1,..., X-n). We say that X is Hoeffding decomposable if, for each n, every square integrable, centered and symmetric statistic based on Xn can be written as an orthogonal sum of n U-statistics with degenerated and symmetric kernels of increasing order. The only two examples of Hoeffding decomposa...
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作者：Funaki, T
作者单位：University of Tokyo
摘要：We consider a system of interacting Brownian particles in R-d with a pairwise potential, which is radially symmetric, of finite range and attains a unique minimum when the distance of two particles becomes a > 0. The asymptotic behavior of the system is studied under the zero temperature limit from both microscopic and macroscopic aspects. If the system is rigidly crystallized, namely if the particles are rigidly arranged in an equal distance a, the crystallization is kept under the evolution ...
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作者：Iksanov, AM; Jurek, ZJ; Schreiber, BM
作者单位：Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; University of Wroclaw
摘要：We prove that the convolution of a selfdecomposable distribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomposable. We will refer to this as the factorization property of a selfdecomposable distribution; let L-f denote the set of all these distributions. The algebraic structure and various characterizations of L-f are studied. Some examples are discussed, the most interesting one being given by the Levy stochastic area int...
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作者：Le Jan, Y; Raimond, O
作者单位：Universite Paris Saclay
摘要：We are interested in stationary fluid random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exist a coalescing flow and a flow of kernels solution of the SDE, a classification is given: All solutions of the SDE ...
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作者：Dolgopyat, D; Kaloshin, V; Koralov, L
作者单位：University System of Maryland; University of Maryland College Park; California Institute of Technology; Princeton University
摘要：We consider a stochastic flow driven by a finite-dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state and the central limit theorem. The proof uses new estimates of the mixing rates of the multi-point motion.
