| 61. |
- Agram, Nacira, et al.
(författare)
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Mean-field backward stochastic differential equations and applications
- 2022
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Ingår i: Systems & control letters (Print). - : Elsevier BV. - 0167-6911 .- 1872-7956. ; 162
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form & nbsp;& nbsp;{dY(t) = -[alpha(1)(t)Y(t) +& nbsp;beta(1)(t)Z(t) +& nbsp;integral(R0 & nbsp;)eta(1)(t,& nbsp;zeta)K(t,& nbsp;zeta)nu(d zeta) +& nbsp;alpha(2)(t)E[Y(t)] +& nbsp;beta(2)(t)E[Z(t)] +& nbsp;integral(R0 & nbsp;)eta(2)(t,& nbsp;zeta)E[K(t,& nbsp;zeta)]nu(d zeta) +& nbsp;gamma(t)]dt + Z(t)dB(t) +& nbsp;integral K-R0 (t,& nbsp;zeta)(N) over tilde(dt, d zeta), t & nbsp;is an element of & nbsp;[0, T].Y(T) =xi.& nbsp;& nbsp;where (Y, Z, K) is the unknown solution triplet, B is a Brownian motion, (N) over tilde is a compensated Poisson random measure, independent of B. We prove the existence and uniqueness of the solution triplet (Y, Z, K) of such systems. Then we give an explicit formula for the first component Y(t) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance.
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| 62. |
- Björklund, Michael, 1981, et al.
(författare)
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Bohr Sets in Triple Products of Large Sets in Amenable Groups
- 2019
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Ingår i: Journal of Fourier Analysis and Applications. - : Springer Science and Business Media LLC. - 1531-5851 .- 1069-5869. ; 25:3, s. 923-936
-
Tidskriftsartikel (refereegranskat)abstract
- We answer a question of Hegyvári and Ruzsa concerning effective estimates of the Bohr-regularity of certain triple sums of sets with positive upper Banach densities in the integers. Our proof also works for any discrete amenable group, and it does not require all addends in the triple products we consider to have positive (left) upper Banach densities; one of the addends is allowed to only have positive upper asymptotic density with respect to a (possibly very sparse) ergodic sequence.
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| 63. |
- Fedosova, K., et al.
(författare)
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High energy asymptotics for the perturbed anharmonic oscillator
- 2021
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Ingår i: Complex Variables and Elliptic Equations. - : Informa UK Limited. - 1747-6933 .- 1747-6941.
-
Tidskriftsartikel (refereegranskat)abstract
- In this article, we study the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise Holder continuous perturbation and investigate how the Holder constant can affect the eigenvalues. More precisely, we derive several first terms in the asymptotic expansion for the eigenvalues.
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| 64. |
- Martinsson, Anders, 1988
(författare)
-
FIRST-PASSAGE PERCOLATION ON CARTESIAN POWER GRAPHS
- 2018
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Ingår i: Annals of Probability. - 2168-894X .- 0091-1798. ; 46:2, s. 1004-1041
-
Tidskriftsartikel (refereegranskat)abstract
- We consider first-passage percolation on the class of "high-dimensional" graphs that can be written as an iterated Cartesian product G square G square...square G of some base graph G as the number of factors tends to infinity. We propose a natural asymptotic lower bound on the first-passage time between (v, v,...,v) and (w, w,...,w) as n, the number of factors, tends to infinity, which we call the critical time t(G)*(v,w). Our main result characterizes when this lower bound is sharp as n ->infinity. As a corollary, we are able to determine the limit of the so-called diagonal time-constant in Z(n) as n ->infinity for a large class of distributions of passage times.
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| 65. |
- Wennberg, Bernt, 1961
(författare)
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Random many-particle systems: applications from biology, and propagation of chaos in abstract models
- 2012
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Ingår i: Rivista di Matematica della Università di Parma. ; 3:2, s. 291-344
-
Konferensbidrag (refereegranskat)abstract
- The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric speciation, i.e. the process in which a genetically homogeneous population is split in two or more different species sharing the same habitat, and models for swarming animals. The second part of the paper deals with abstract many particle systems and methods for rigorously deriving mean field models.
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| 66. |
- Wennberg, Bernt, 1961, et al.
(författare)
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The Kac master equation with unbounded collision rate
- 2009
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Ingår i: Markov Processes and Related Fields. - 1024-2953. ; 15:2, s. 125-148
-
Tidskriftsartikel (refereegranskat)abstract
- The Kac model is a Markov jump process on the sphere $\sum_{j=1}^{N} v_j^2$. The model was conceived as model for an N-particle system with pairwise interactions, and hence the jumps involve only pairs of coordinates, $(v_i, v_j )$. This paper deals with Kac models with unbounded jump rates. We prove that the processes are Feller processes, and introduce a diusion approximation that is useful for numerical simulation of the processes. We also study the spectral gap of the Markov generators, using the methods developed by Carlen, Carvalho and Loss.
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| 67. |
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| 68. |
- Ahmad, M. Rauf, et al.
(författare)
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Tests for high-dimensional covariance matrices using the theory of U-statistics
- 2015
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Ingår i: Journal of Statistical Computation and Simulation. - : Informa UK Limited. - 0094-9655 .- 1563-5163. ; 85:13, s. 2619-2631
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Tidskriftsartikel (refereegranskat)abstract
- Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.
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| 69. |
- Berman, Robert, 1976
(författare)
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The spherical ensemble and quasi-Monte-Carlo designs
- 2023
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Ingår i: Constructive Approximation. - 0176-4276 .- 1432-0940.
-
Tidskriftsartikel (refereegranskat)abstract
- The spherical ensemble is a well-known ensemble of N repulsive points on the twodimensional sphere, which can realized in various ways (as a random matrix ensemble, a determinantal point process, a Coulomb gas, a Quantum Hall state...). Here we show that the spherical ensemble enjoys remarkable convergence properties from the point of view of numerical integration. More precisely, it is shown that the numerical integration rule corresponding to N nodes on the two-dimensional sphere sampled in the spherical ensemble is, with overwhelming probability, nearly a quasi-Monte-Carlo design in the sense of Brauchart-Saff-Sloan-Womersley for any smoothness parameter s = 2. The key ingredient is a new explicit sub-Gaussian concentration of measure inequality for the spherical ensemble.
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| 70. |
- Bolin, David, 1983, et al.
(författare)
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The Rational SPDE Approach for Gaussian Random Fields With General Smoothness
- 2020
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Ingår i: Journal of Computational and Graphical Statistics. - : Informa UK Limited. - 1061-8600 .- 1537-2715. ; 29:2, s. 274-85
-
Tidskriftsartikel (refereegranskat)abstract
- A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form , where is Gaussian white noise, L is a second-order differential operator, and is a parameter that determines the smoothness of u. However, this approach has been limited to the case , which excludes several important models and makes it necessary to keep beta fixed during inference. We propose a new method, the rational SPDE approach, which in spatial dimension is applicable for any , and thus remedies the mentioned limitation. The presented scheme combines a finite element discretization with a rational approximation of the function to approximate u. For the resulting approximation, an explicit rate of convergence to u in mean-square sense is derived. Furthermore, we show that our method has the same computational benefits as in the restricted case . Several numerical experiments and a statistical application are used to illustrate the accuracy of the method, and to show that it facilitates likelihood-based inference for all model parameters including beta. for this article are available online.
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