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作者：Roitershtein, Alexander
作者单位：University of British Columbia
摘要：We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344-353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344-353], the branching process is subcritical in the sense that it converges to a proper limit law. We complement this result by a strong law of large numbers and a central limit theorem for the partial sums of the process. In addition, we study the asymptotic behavior of oscill...
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作者：Wang, Feng-Yu
作者单位：Beijing Normal University
摘要：By using coupling and Girsanov transformations, the dimension-free Harnack inequality and the strong Feller property are proved for transition semigroups of solutions to a class of stochastic generalized porous media equations. As applications, explicit upper bounds of the L-P-norm of the density as well as hypercontractivity, ultracontractivity and compactness of the corresponding semigroup are derived.
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作者：Greven, A.; Den Hollander, F.
作者单位：University of Erlangen Nuremberg; Leiden University; Leiden University - Excl LUMC
摘要：Let ({X-i(t)}(i is an element of Z)(d))(t >= 0) be the system of interacting diffusions on [0, infinity) defined by the following collection of coupled stochastic differential equations: dX(i) (t) = Sigma(d)(j is an element of Z) a(i, j)[X-j(t) - X-i(t)]dt + root bX(i)(t)(2)dW(i)(t), i is an element of Z(d), t >= 0. Here, a(., .) is an irreducible random walk transition kernel on Z(d) x Z(d), b is an element of (0, infinity) is a diffusion parameter, and ({W-i(t)}(i is an element of Z)(d))(t >...
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作者：Doney, Ron; Maller, Ross
作者单位：University of Manchester; Australian National University; Australian National University
摘要：Let R-n = max(0 <= j <= n) S-j - S-n be a random walk S-n reflected in its maximum. Except in the trivial case when P(X >= 0) = 1, R-n will pass over a horizontal boundary of any height in a finite time, with probability 1. We extend this by giving necessary and sufficient conditions for finiteness of passage times of R-n above certain curved (power law) boundaries, as well. The intuition that a degree of heaviness of the negative tail of the distribution of the increments of S-n is necessary ...
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作者：Cerny, Ales; Kallsen, Jan
作者单位：City St Georges, University of London; Technical University of Munich; Aalto University
摘要：We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure P* which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to P* coincides with the variance-optimal martingale measure relative to the original probability measure P.
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作者：Barany, Imre; Vu, Van
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of London; University College London; Rutgers University System; Rutgers University New Brunswick
摘要：Choose n random, independent points in R-d according to the standard normal distribution. Their convex hull K-n is the Gaussian random polytope. We prove that the volume and the number of faces of K-n satisfy the central limit theorem, settling a well-known conjecture in the field.
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作者：Balazs, M.; Rassoul-Agha, F.; Seppaelaeinen, T.; Sethuraman, S.
作者单位：Budapest University of Technology & Economics; University of Wisconsin System; University of Wisconsin Madison; Utah System of Higher Education; University of Utah; Iowa State University
摘要：We give a construction of the zero range and bricklayers' processes in the totally asymmetric, attractive case. The novelty is that we allow jump rates to grow exponentially. Earlier constructions have permitted at most linearly growing rates. We also show the invariance and extremality of a natural family of i.i.d. product measures indexed by particle density. Extremality is proved with an approach that is simpler than existing ergodicity proofs.
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作者：van Neerven, J. M. A. M.; Veraar, M. C.; Weis, L.
作者单位：Delft University of Technology; Helmholtz Association; Karlsruhe Institute of Technology
摘要：In this paper we construct a theory of stochastic integration of processes with values in L(H, E), where H is a separable Hilbert space and E is a UMD Banach space (i.e., a space in which martingale differences are unconditional). The integrator is an H-cylindrical Brownian motion. Our approach is based on a two-sided L-p-decoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic integration of L(H, E)-valued functions introduced recently by two of the...
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作者：Brydges, David; van der Hofstad, Remco; Koenig, Wolfgang
作者单位：University of British Columbia; Eindhoven University of Technology; Leipzig University
摘要：We investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density of all local times on the range, at any fixed time. We use standard tools from the theory of stochastic processes and finite-dimensional complex calculus. We apply this formula in the following directions: (1) we derive large deviation upper estimates for the normalized local times beyond the expon...
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作者：Bai, Z. D.; Miao, B. Q.; Pan, G. M.
作者单位：Northeast Normal University - China; Northeast Normal University - China; Chinese Academy of Sciences; University of Science & Technology of China, CAS; National University of Singapore
摘要：Let {X-ij}, i, j = .... be a double array of i.i.d. complex random variables with EX11 =0, E vertical bar X-11 vertical bar(2) = 1 and E vertical bar X-11 vertical bar(4) < infinity, and let A(n) = 1/N T-n(1/2) X-n (XnTn1/2)-T-*, where T-n(1/2) is the square root of a nonnegative definite matrix T-n and X-n is the n x N matrix of the upper-left corner of the double array. The matrix A(n) can be considered as a sample covariance matrix of an i.i.d. sample from a population with mean zero and co...
