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The Annals of Statistics, ISSN 0090-5364, 8/2005, Volume 33, Issue 4, pp. 1617 - 1642
Journal Article
Russian Journal of Numerical Analysis and Mathematical Modelling, ISSN 0927-6467, 12/2019, Volume 34, Issue 6, pp. 327 - 338
The problem of constructing a numerically realizable model of a three-dimensional homogeneous random field in a layer 0 < < with given one-dimensional... 
65C20 | Random field | 68U20 | gamma distribution | randomization | 65C05 | correlation function
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 06/2018, Volume 75, Issue 3, pp. 1776 - 1807
In this paper, we are interested in the exact simulation of a class of piecewise deterministic Markov processes. We show how to perform an efficient thinning... 
Piecewise deterministic Markov process | Thinning | Channel noise | Exact simulation | Neural model | ACTION-POTENTIALS | MATHEMATICS, APPLIED | BEHAVIOR | HODGKIN-HUXLEY EQUATIONS | NERVE MEMBRANE | MODEL | FLUCTUATIONS | CONVERGENCE | Markov processes | Models | Algorithms | Analysis | Mathematics - Probability | Probability | Mathematics
Journal Article
Monte Carlo Methods and Applications, ISSN 0929-9629, 12/2019, Volume 25, Issue 4, pp. 291 - 305
We develop a numerical algorithm for predicting prices and Greeks of equity-linked securities (ELS) with a knock-in barrier at any time over the total time... 
65C20 | 91G60 | 60J70 | 65C05 | option pricing | Equity-linked securities | Monte Carlo simulation | Brownian bridge
Journal Article
Journal of Applied Mathematics, Statistics and Informatics, ISSN 1339-0015, 12/2019, Volume 15, Issue 2, pp. 5 - 14
In recent years, a lot of effort has been put into finding suitable mathematical models that fit historical data set. Such models often include coefficients... 
65C20 | 91B64 | Systems modelling | integral method | linear regression | 34C60 | error minimization | systems modelling | 65c20 | 91b64 | 34c60
Journal Article
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, ISSN 0022-3239, 06/2019, Volume 181, Issue 3, pp. 1015 - 1032
We present an optimal hybrid control approach to the problem of stochastic route planning for sailing boats, especially in short course fleet races, in which... 
65C20 | MATHEMATICS, APPLIED | 93E20 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Optimal control | 65N06 | Hybrid systems | Route planning | Performance indices | Sailing | Boats | Hybrid control | Mathematical models | Maneuvers
Journal Article
Computing, ISSN 0010-485X, 08/2003, Volume 71, Issue 1, pp. 65 - 87
We consider the numerical integration of multivariate functions defined over the unit hypercube. Here, we especially address the high–dimensional case, where... 
65D30 | 65C20 | ComputerScience | adaptivity | multivariate numerical integration | curse of dimension | 65U05 | 65Y20 | Multivariate numerical integration | Curse of dimension | Adaptivity | INTEGRATION | SPACES | SPARSE GRIDS | COMPUTER SCIENCE, THEORY & METHODS | ALGORITHMS | DERIVATIVES | EQUATION | Algorithms
Journal Article
The Annals of Applied Probability, ISSN 1050-5164, 12/2015, Volume 25, Issue 6, pp. 3095 - 3138
In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their... 
Monte Carlo methods | Stochastic differential equations | Parametrix | Density | TRANSITION DENSITIES | STOCHASTIC DIFFERENTIAL-EQUATIONS | DIFFUSIONS | density | EXPANSION | LOCAL LIMIT-THEOREMS | STATISTICS & PROBABILITY | ERROR | stochastic differential equations | Mathematics - Probability | Probability | Mathematics | 65C20 | 65C30 | 35K15 | 65C05 | 35K10
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 11/2018, Volume 116, pp. 348 - 357
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 07/2018, Volume 95, Issue 6-7, pp. 1210 - 1221
In this paper, a numerical method is proposed for solving nonlinear variable-order space fractional diffusion equations. The method is based on the reproducing... 
65C20 | Reproducing kernel | nonlinear | diffusion equations | 46E22 | 34A08 | MATHEMATICS, APPLIED | TURNING-POINT PROBLEMS | NUMERICAL-METHOD | BOUNDARY-VALUE-PROBLEMS | FUNCTIONAL-DIFFERENTIAL EQUATIONS | Iterative methods | Mathematical analysis | Numerical analysis
Journal Article
Numerical Algorithms, ISSN 1017-1398, 10/2019, Volume 82, Issue 2, pp. 719 - 728
In this paper, the system of nonlinear inequalities is considered. The problem is approximated by the parameterized smooth equations which is formed by... 
65C20 | 65L05 | Homotopy method | Global convergence | Algorithms | Algebra | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | 65H10 | System of inequalities | MATHEMATICS, APPLIED | FINITE NUMBER | ALGORITHM
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 08/2018, Volume 95, Issue 8, pp. 1565 - 1582
We compare the CPU effort and pricing biases of seven Fourier-based implementations. Our analyses show that truncation and discretization errors significantly... 
65C20 | Fourier transforms | 30E10 | 65T50 | Option pricing | speed comparisons | pricing errors | jump processes | 60H35 | Mathematical models | Numerical analysis | Fast Fourier transformations | Pricing | Quantitative Finance - Computational Finance
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 03/2016, Volume 56, Issue 1, pp. 151 - 162
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s10543-015-0549-x In this... 
Numerical methods for stochastic differential equations | Discontinuous drift | Stochastic differential equations | Monte Carlo method | Methods | Mathematics - Probability
Journal Article
Arabian Journal of Mathematics, ISSN 2193-5343, 6/2016, Volume 5, Issue 2, pp. 77 - 86
The goal of this paper is to give useful method for solving a problem in biologic system that is formulated by stochastic Volterra integral equations. Here, we... 
65C20 | 65C30 | 60H20 | 37N25 | Mathematics, general | Mathematics | 60H35
Journal Article
Journal of Inverse and Ill-posed Problems, ISSN 0928-0219, 06/2019, Volume 27, Issue 3, pp. 353 - 366
In this paper, we consider the non-recombining trinomial tree pricing model under the volatility, which is a function of time, establish the option pricing... 
65C20 | 91G60 | Volatility | nonlinear unconstrained optimization | option pricing | non-recombining trinomial tree model | calibration | Algorithms | Model testing | Pricing | Pricing policies | Calibration | Optimization
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 03/2013, Volume 19, Issue 3, pp. 466 - 490
For stochastic differential equations (SDEs) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient, the classical explicit... 
tamed Milstein method | one-sided Lipschitz condition | commutative noise | strong convergence | superlinearly growing coefficient | 65C20 | SCHEME | MATHEMATICS, APPLIED | 65L20 | EULER | 60H35 | STRONG-CONVERGENCE | Difference equations | Mathematical analysis | Differential equations | Exact solutions | Mathematical models | Computational efficiency | Stochasticity | Convergence
Journal Article
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