Browsing Matematisk institutt by Title
Now showing items 3744-3763 of 3782
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(Research report / Forskningsrapport, 2006)We consider higher-order Camassa--Holm equations describing exponential curves of the manifold of smooth orientation preserving diffeomorphisms of the unit circle in the plane. We establish the existence of a strongly ...
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(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2023)
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(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)In this paper we study the Ostrovsky–Hunter equation for the case where the flux function f(x, u) may depend on the spatial variable with certain smoothness. Our main results are that if the flux function is smooth enough ...
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(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2022)We consider nonlinear scalar conservation laws posed on a network. We define an entropy condition for scalar conservation laws on networks and establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying ...
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(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)We investigate a class of scalar conservation laws on manifolds driven by multiplicative Gaussian (Itô) noise. The Cauchy problem defined on a Riemanian manifold is shown to be well-posed. We prove existence of generalized ...
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(Research report / Forskningsrapport, 1992)
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(Research report / Forskningsrapport, 2004)We show existence of a unique, regular global solution of the parabolic-elliptic system $u_t +f(t,x,u)_x+g(t,x,u)+P_x=(a(t,x) u_x)_x$ and $-P_{xx}+P=h(t,x,u,u_x)+k(t,x,u)$ with initial data $u|_{t=0} = u_0$. Here ...
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(Research report / Forskningsrapport, 1996)
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(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)Cox’s proportional hazards regression model is the standard method for modelling censored life-time data with covariates. In its standard form, this method relies on a semiparametric proportional hazards structure, leaving ...
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(Research report / Forskningsrapport, 2001)We consider optimal control problems where the state X(t) at time t of the system is given by a stochastic differential delay equation. The growth at time t not only depends on the present value X(t), but also on X(t-d) ...
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(Research report / Forskningsrapport, 1985)
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(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2020)Let X be a Riemannian manifold and xn a sequence of points in X. Assume that we know a priori some properties of the set A of cluster points of xn. The question is under what conditions that xn will converge. An answer to ...
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(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2019)Principal component analysis (PCA) is often used in anomaly detection and statistical process control tasks. For bivariate normal data, we prove that the minor projection (the least varying projection) of the PCA‐rotated ...
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(Research report / Forskningsrapport, 2002)
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(Chapter / Bokkapittel / AcceptedVersion; Peer reviewed, 2015)We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, Hida-Malliavin calculus and the Donsker delta function.
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A White Noise Approach to Stochastic Differential Equations Driven by Wiener and Poisson Processes (Research report / Forskningsrapport, 1998)
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(Research report / Forskningsrapport, 1999)
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(Research report / Forskningsrapport, 2007)
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(Research report / Forskningsrapport, 2002)We develop a white noise theory for Poisson random measures associated with a Lévy process. The starting point of this theory is a chaos expansion with kernels of polynomial type. We use this to construct the white noise ...
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(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)We study the Whitehead torsion of inertial h-cobordisms, continuing an investigation started in [12]. Of particular interest is a nested sequence of subsets of the Whitehead group, and a number of examples are given to ...