| 1. |
- Chiacchio, Marc, et al.
(författare)
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On the links between meteorological variables, aerosols, and tropical cyclone frequency in individual ocean basins
- 2017
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Ingår i: Journal of Geophysical Research. - : American Geophysical Union (AGU). - 0148-0227 .- 2156-2202. ; 122:2, s. 802-822
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 2. |
- Lundström, Niklas, 1980-, et al.
(författare)
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Stochastic and partial differential equations on non-smooth time-dependent domains
- 2019
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Ingår i: Stochastic Processes and their Applications. - : Elsevier. - 0304-4149 .- 1879-209X. ; 129:4, s. 1097-1131
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we consider non-smooth time-dependent domains whose boundary is W1,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.
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| 3. |
- Nyström, Kaj, 1969-, et al.
(författare)
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On Monte Carlo algorithms applied to Dirichlet problems for parabolic operators in the setting of time-dependent domains
- 2009
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Ingår i: Monte Carlo Methods and Applications. - Berlin New York : de Gruyter. - 1569-3961. ; 15, s. 11-47
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Tidskriftsartikel (refereegranskat)abstract
- Dirichlet problems for second order parabolic operators in space-time domains Ω⊂ Rn+1 are of paramount importance in analysis, partial differential equations and applied mathematics. These problems can be approached in many different ways using techniques from partial differential equations, potential theory, stochastic differential equations, stopped diffusions and Monte Carlo methods. The performance of any technique depends on the structural assumptions on the operator, the geometry and smoothness properties of the space-time domain Ω, the smoothness of the Dirichlet data and the smoothness of the coefficients of the operator under consideration. In this paper, which mainly is of numerical nature, we attempt to further understand how Monte Carlo methods based on the numerical integration of stochastic differential equations perform when applied to Dirichlet problems for uniformly elliptic second order parabolic operators and how their performance vary as the smoothness of the boundary, Dirichlet data and coefficients change from smooth to non-smooth. Our analysis is set in the genuinely parabolic setting of time-dependent domains, which in itself adds interesting features previously only modestly discussed in the literature. The methods evaluated and discussed include elaborations on the non-adaptive method proposed by Gobet [4] based on approximation by half spaces and exit probabilities and the adaptive method proposed in [3] for weak approximation of stochastic differential equations.
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| 4. |
- Önskog, Thomas, 1979-
(författare)
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Existence of pathwise unique Langevin processes on polytopes with perfect reflection at the boundary
- 2013
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Ingår i: Statistics and Probability Letters. - : Elsevier. - 0167-7152 .- 1879-2103. ; 83:10, s. 2211-2219
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Tidskriftsartikel (refereegranskat)abstract
- Exploiting an explicit projection from the real line into an interval, we prove existence and pathwise uniqueness of one-dimensional Langevin processes confined to an interval with perfect reflection at the boundary. This result is subsequently generalized to multidimensional Langevin processes confined to box domains or general polytopes.
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| 5. |
- Önskog, Thomas, 1979-, et al.
(författare)
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Pricing and hedging of financial derivatives using a posteriori error estimates and adaptive methods for stochastic differential equations
- 2010
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 235, s. 563-592
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 6. |
- Önskog, Thomas, 1979-
(författare)
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The Skorohod problem and weak approximation of stochastic differential equations in time-dependent domains
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of a summary and four scientific articles. All four articles consider various aspects of stochastic differential equations and the purpose of the summary is to provide an introduction to this subject and to supply the notions required in order to fully understand the articles. In the first article we conduct a thorough study of the multi-dimensional Skorohod problem in time-dependent domains. In particular we prove the existence of cádlág solutions to the Skorohod problem with oblique reflection in time-independent domains with corners. We use this existence result to construct weak solutions to stochastic differential equations with oblique reflection in time-dependent domains. In the process of obtaining these results we also establish convergence results for sequences of solutions to the Skorohod problem and a number of estimates for solutions, with bounded jumps, to the Skorohod problem. The second article considers the problem of determining the sensitivities of a solution to a second order parabolic partial differential equation with respect to perturbations in the parameters of the equation. We derive an approximate representation of the sensitivities and an estimate of the discretization error arising in the sensitivity approximation. We apply these theoretical results to the problem of determining the sensitivities of the price of European swaptions in a LIBOR market model with respect to perturbations in the volatility structure (the so-called ‘Greeks’). The third article treats stopped diffusions in time-dependent graph domains with low regularity. We compare, numerically, the performance of one adaptive and three non-adaptive numerical methods with respect to order of convergence, efficiency and stability. In particular we investigate if the performance of the algorithms can be improved by a transformation which increases the regularity of the domain but, at the same time, reduces the regularity of the parameters of the diffusion. In the fourth article we use the existence results obtained in Article I to construct a projected Euler scheme for weak approximation of stochastic differential equations with oblique reflection in time-dependent domains. We prove theoretically that the order of convergence of the proposed algorithm is 1/2 and conduct numerical simulations which support this claim.
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| 7. |
- Önskog, Thomas, 1979-, et al.
(författare)
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Weak approximation of obliquely reflected diffusions in time-dependent domains
- 2010
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Ingår i: Journal of Computational Mathematics. - : Global Science Press. - 0254-9409 .- 1991-7139. ; 28:5, s. 579-605
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 8. |
- Önskog, Thomas, 1979-, et al.
(författare)
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The Skorohod oblique reflection problem in time-dependent domains
- 2010
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Ingår i: Annals of Probability. - : Project Euclid. - 0091-1798 .- 2168-894X. ; 38:6, s. 2170-2223
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Tidskriftsartikel (refereegranskat)abstract
- 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 and further investigated by P.-L. Lions and A.-S. Sznitman 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 càdlàg solutions (x, λ) to the Skorohod problem, with oblique reflection, for (D,,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.
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