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  • 1. Chiacchio, Marc
    et al.
    Pausata, Fransesco S. R.
    Messori, Gabriele
    Hannachi, Abdel
    Chin, Mian
    Önskog, Thomas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Ekman, Annica M. L.
    Barrie, Leonard
    On the links between meteorological variables, aerosols, and tropical cyclone frequency in individual ocean basins2017Ingår i: Journal of Geophysical Research, ISSN 0148-0227, E-ISSN 2156-2202, Vol. 122, s. 802-822Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A generalized linear model based on Poisson regression has been used to assess the impact of environmental variables modulating tropical cyclone frequency in six main cyclone development areas: the East Pacific, West Pacific, North Atlantic, North Indian, South Indian, and South Pacific. The analysis covers the period 1980-2009 and focuses on widely used meteorological parameters including wind shear, sea surface temperature, and relative humidity from different reanalyses as well as aerosol optical depth for different compounds simulated by the Goddard Chemistry Aerosol Radiation and Transport model. Circulation indices are also included. Cyclone frequency is obtained from the International Best Track Archive for Climate Stewardship. A strong link is found between cyclone frequency and the relative sea surface temperature, Atlantic Meridional Mode, and wind shear with significant explained log likelihoods in the North Atlantic of 37%, 27%, and 28%, respectively. A significant impact of black carbon and organic aerosols on cyclone frequency is found over the North Indian Ocean, with explained log likelihoods of 27%. A weaker but still significant impact is found for observed dust aerosols in the North Atlantic with an explained log likelihood of 11%. Changes in lower stratospheric temperatures explain 28% of the log likelihood in the North Atlantic. Lower stratospheric temperatures from a subset of Coupled Model Intercomparison Project Phase 5 models properly simulate the warming and subsequent cooling of the lower stratosphere that follows a volcanic eruption but underestimates the cooling by about 0.5 degrees C.

  • 2. Lundström, Niklas L. P.
    et al.
    Önskog, Thomas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Stochastic and partial differential equations on non-smooth time-dependent domains2019Ingår i: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 129, nr 4, s. 1097-1131Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article, we consider non-smooth time-dependent domains whose boundary is W^{1,p} in time and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic differential equations with oblique reflection. Secondly, we prove, using the theory of viscosity solutions, a comparison principle for fully nonlinear second-order parabolic partial differential equations with oblique derivative boundary conditions. As a consequence, we obtain uniqueness, and, by barrier construction and Perron’s method, we also conclude existence of viscosity solutions. Our results generalize two articles by Dupuis and Ishii to time-dependent domains.

  • 3. Nyström, Kaj
    et al.
    Önskog, Thomas
    Pricing and hedging of financial derivatives using a posteriori error estimates and adaptive methods for stochastic di¤erential equations.2010Ingår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 235, s. 563-592Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The efficient and accurate calculation of sensitivities of the price of financial derivatives with respect to perturbations of the parameters in the underlying model, the so-called ‘Greeks’, remains a great practical challenge in the derivative industry. This is true regardless of whether methods for partial differential equations or stochastic differential equations (Monte Carlo techniques) are being used. The computation of the ‘Greeks’ is essential to risk management and to the hedging of financial derivatives and typically requires substantially more computing time as compared to simply pricing the derivatives. Any numerical algorithm (Monte Carlo algorithm) for stochastic differential equations produces a time-discretization error and a statistical error in the process of pricing financial derivatives and calculating the associated ‘Greeks’. In this article we show how a posteriori error estimates and adaptive methods for stochastic differential equations can be used to control both these errors in the context of pricing and hedging of financial derivatives. In particular, we derive expansions, with leading order terms which are computable in a posteriori form, of the time-discretization errors for the price and the associated ‘Greeks’. These expansions allow the user to simultaneously first control the time-discretization errors in an adaptive fashion, when calculating the price, sensitivities and hedging parameters with respect to a large number of parameters, and then subsequently to ensure that the total errors are, with prescribed probability, within tolerance.

  • 4. Nyström, Kaj
    et al.
    Önskog, Thomas
    Remarks on the Skorohod problem and reflected Lévy driven SDEs in time-dependent domains2015Ingår i: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 87, nr 5, s. 747-765Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the Skorohod problem for cadlag functions, and the subsequent construction of solutions to normally reflected stochastic differential equations driven by Levy processes, in the setting of non-smooth and time-dependent domains.

  • 5. Nyström, Kaj
    et al.
    Önskog, Thomas
    The Skorohod oblique reflection problem in time-dependent domains2010Ingår i: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 38, nr 6, s. 2170-2223Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The deterministic Skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection. In the form studied here, the multidimensional Skorohod problem was introduced, in time-independent domains, by H. Tanaka [61] and further investigated by P.-L. Lions and A.-S. Sznitman [42] in their celebrated article. Subsequent results of several researchers have resulted in a large literature on the Skorohod problem in time-independent domains. In this article we conduct a thorough study of the multidimensional Skorohod problem in time-dependent domains. In particular, we prove the existence of cadlag solutions (x, lambda) to the Skorohod problem, with oblique reflection, for (D, Gamma, w) assuming, in particular, that D is a time-dependent domain (Theorem 1.2). In addition, we prove that if w is continuous, then x is continuous as well (Theorem 1.3). Subsequently, we use the established existence results to construct solutions to stochastic differential equations with oblique reflection (Theorem 1.9) in time-dependent domains. In the process of proving these results we establish a number of estimates for solutions to the Skorohod problem with bounded jumps and, in addition, several results concerning the convergence of sequences of solutions to Skorohod problems in the setting of time-dependent domains.

  • 6. Nyström, Kaj
    et al.
    Önskog, Thomas
    Weak approximation of obliquely reflected diffusions in time-dependent domains.2010Ingår i: Journal of Computational Mathematics, ISSN 0254-9409, E-ISSN 1991-7139, Vol. 28, nr 5, s. 579-605Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In an earlier paper, we proved the existence of solutions to the Skorohod problem with oblique reflection in time-dependent domains and, subsequently, applied this result to the problem of constructing solutions, in time-dependent domains, to stochastic differential equations with oblique reflection. In this paper we use these results to construct weak approximations of solutions to stochastic differential equations with oblique reflection, in time-dependent domains in R-d, by means of a projected Euler scheme. We prove that the constructed method has, as is the case for normal reflection and time-independent domains, an order of convergence equal to 1/2 and we evaluate the method empirically by means of two numerical examples. Furthermore, using a well-known extension of the Feynman-Kac formula, to stochastic differential equations with reflection, our method gives, in addition, a Monte Carlo method for solving second order parabolic partial differential equations with Robin boundary conditions in time-dependent domains.

  • 7. Zhang, Jun
    et al.
    Önskog, Thomas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Langevin equation elucidates the mechanism of the Rayleigh-Benard instability by coupling molecular motions and macroscopic fluctuations2017Ingår i: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, nr 4, artikel-id 043104Artikel i tidskrift (Refereegranskat)
  • 8.
    Önskog, Thomas
    Uppsala university.
    Existence of pathwise unique Langevin processes on polytopes with perfect reflection at the boundary2013Ingår i: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 83, s. 2211-2219Artikel i tidskrift (Refereegranskat)
  • 9.
    Önskog, Thomas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Lundström, Niklas L. P.
    Olofsson, Marcus
    Existence, uniqueness and regularity of solutions to systems of nonlocal obstacle problems related to optimal switching2019Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study viscosity solutions to a system of nonlinear degenerate parabolic partial integro-differential equations with interconnected obstacles. This type of problem occurs in the context of optimal switching problems when the dynamics of the underlying state variableis described by an n-dimensional Lévy process. We first establish a continuous dependence estimate for viscosity sub- and supersolutions to the system under mild regularity, growth and structural assumptions on the partial integro-differential operator and on the obstacles and terminal conditions. Using the continuous dependence estimate, we obtain the comparison principle and uniqueness of viscosity solutions as well as Lipschitz regularity in the spatial variables. Our main contribution is construction of suitable families of viscosity sub- and supersolutions which we use as “barrier functions” to prove Hölder continuity in the time variable, and, through Perron’s method, existence of a unique viscosity solution. This paper generalizes parts of the results of Biswas, Jakobsen and Karlsen (2010) [BJK10] and of Lundström, Nyström and Olofsson (2014) [LNO14, LNO14b] to hold for more general systems of equations.

  • 10.
    Önskog, Thomas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik. Stockholm University.
    Zhang, Jun
    An accurate treatment of diffuse reflection boundary conditions for a stochastic particle Fokker-Planck algorithm with large time steps2015Ingår i: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 440, s. 139-146Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we present a stochastic particle algorithm for the simulation of flows of wall-confined gases with diffuse reflection boundary conditions. Based on the theoretical observation that the change in location of the particles consists of a deterministic part and a Wiener process if the time scale is much larger than the relaxation time, a new estimate for the first hitting time at the boundary is obtained. This estimate facilitates the construction of an algorithm with large time steps for wall-confined flows. Numerical simulations verify that the proposed algorithm reproduces the correct boundary behaviour.

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