Browsing NTNU Open by Author "Jakobsen, Espen Robstad"
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A spectral method for fractional porous medium equations
Bærland, Trygve (Master thesis, 2015)This master's thesis considers the fractional general porous medium equation; a nonlocal equation with nonlinear diffusivity. Properties of the nonlocal operator are derived. Existence of distributional solutions are proved, ... 
Discontinous Galerkin Methods for Conservation Laws,  with and without fractional diffusion
Sigurdsson, Alexander N. (Master thesis, 2018)This thesis was submitted on July 5'th 2018 as the Master's thesis for Alexander N Sigurdsson in Industrial Mathematics at the Department of Mathematical Sciences at The Norwegian University of Science and Technology (NTNU). ... 
Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems
Jakobsen, Espen Robstad; Picarelli, Athena; Reisinger, Christoph (Journal article; Peer reviewed, 2019)In N. V. Krylov, Approximating value functions for controlled degenerate diffusion processes by using piecewise constant policies, Electron. J. Probab., 4(2), 1999, it is proved under standard assumptions that the value ... 
L1 contraction for bounded (nonintegrable) solutions of degenerate parabolic equations
Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 20141211)We obtain new L1 contraction results for bounded entropy solutions of Cauchy problems for degenerate parabolic equations. The equations we consider have possibly strongly degenerate local or nonlocal diffusion terms. As ... 
L1 semigroup generation for FokkerPlanck operators associated with general Levy driven SDEs
Chen, Linghua; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2018)We prove a new generation result in L 1 for a large class of nonlocal operators with nondegenerate local terms. This class contains the operators appearing in FokkerPlanck or Kolmogorov forward equations associated ... 
The Liouville theorem and linear operators satisfying the maximum principle.
Alibaud, Nathael; del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Peer reviewed; Journal article, 2020)A result by Courrège says that linear translation invariant operators satisfy the maximum principle if and only if they are of the form L = Lσ,b + Lμ where Lσ,b[u](x) = tr(σσTD2u(x)) + b · Du(x) and Lμ[u](x) = Rd\{0} u(x ... 
The Liouville theorem and linear operators satisfying the maximum principle.
Alibaud, Nathael; del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Peer reviewed; Journal article, 2020)A result by Courrège says that linear translation invariant operators satisfy the maximum principle if and only if they are of the form L = Lσ,b + Lμ where Lσ,b[u](x) = tr(σσTD2u(x)) + b · Du(x) and Lμ[u](x) ... 
Maximum Principles for Differential Equations
Duguma, Tadesse Guluma (Master thesis, 2014)maximum principle is one among the most useful and best known tools used in the study of partial differential equations. This principle is a generalization of the well known fact of calculus that any function u(x) which ... 
Nonlinear fractional convectiondiffusion equations, with nonlocal and nonlinear fractional diffusion
Endal, Jørgen (Master thesis, 2013)We study nonlinear fractional convectiondiffusion equations with nonlocal and nonlinear fractional diffusion. By the idea of Kru\v{z}kov (1970), entropy sub and supersolutions are defined in order to prove wellposedness ... 
Nonlinear integrodifferential Equations: Numerical Solutions by using Spectral Methods
Davidsen, SteinOlav Hagen (Master thesis, 2013)This article deals with numerical solutions of nonlinear integrodifferential convectiondiffusion equations using spectral methods. More specifically, the spectral vanishing viscosity method is introduced and analyzed to ... 
Numerical Methods and Brute Force Optimisation for a General Formulation of the Mean Field Game Equations
Husby, Snorre Alexander Berthelsen (Master thesis, 2015)This thesis considers the numerical solution of a general formulation of the mean field game (MFG) equations. MFG are a relatively new field with few general results but with many modelling applications. The MFG equations ... 
Numerical Methods for Valuation and Optimal Operation of Natural Gas Storage
Følstad, Erik Magnus G. (Master thesis, 2015)The thesis describes different approaches for solving numerically a PDE model for the valuation and optimal operation of a natural gas storage facility, characterized as a Hamilton Jacobi Bellman (HJB) equation. The HJB ... 
Numerical Models for Jump Diffusion Processes: A Finite Element Approach
Hornæs, Kristin Kaarbø (Master thesis, 2013)In this thesis we propose a finite element solution to the jump diffusion problem for pricing options. We focus on assets following CGMY processes and formulate the problem in weak bilinear form. In the case where the CGMY ... 
On Degenerate Parabolic Problems with Local and Nonlocal Diffusion
Endal, Jørgen (Doctoral theses at NTNU;2017:229, Doctoral thesis, 2017) 
On distributional solutions of local and nonlocal problems of porous medium type
del Teso Mendez, Felix; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2017)We present a theory of wellposedness and a priori estimates for bounded distributional (or very weak) solutions of ∂tu − L σ,µ[ϕ(u)] = g(x, t) in R N (0.1) × (0, T ), where ϕ is merely continuous and nondecreasing and L ... 
On nonlocal quasilinear equations and their local limits
Chasseigne, Emmanuel; Jakobsen, Espen Robstad (Journal article, 2017)We introduce a new class of quasilinear nonlocal operators and study equations involving these operators. The operators are degenerate elliptic and may have arbitrary growth in the gradient. Included are new nonlocal ... 
On numerical density approximations of solutions of SDEs with unbounded coefficients
Chen, Linghua; Jakobsen, Espen Robstad; Næss, Arvid (Journal article, 2017)We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and ... 
On the theory and numerical analysis of viscosity solutions
Jakobsen, Espen Robstad (Dr. ingeniøravhandling, 0809103X; 2001:95, Doctoral thesis, 2001) 
On the wellposedness of solutions with finite energy for nonlocal equations of porous medium type
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Chapter, 2018)We study wellposedness and equivalence of different notions of solutions with finite energy for nonlocal porous medium type equations of the form ∂tu − Aϕ(u) = 0. These equations are possibly degenerate nonlinear diffusion ... 
Pricing European Options with Lévy Market Models and Deep Learning
Uv, Julie Johanne (Master thesis, 2019)I denne oppgaven har fem Lévymodeller og et kunstig nevralt nettverk blitt implementert for å sammenligne prising av europeiske kjøpsopsjoner mot den geometrisk brownske bevegelsesdynamikken i BlackScholesformelen. ...