Stochastic differential

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  • This research monograph concerns the design and analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes and Poisson processes or Poisson jump measures. In financial and actuarial modeling and other areas of application, such jump diffusions are often used to describe the dynamics of various state variables. In finance these may represent, for instance, asset prices, credit ratings, stock indices, interest rates, exchange rates or commodity prices.

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Square-mean almost automorphic mild solutions to some stochastic differential equations in a Hilbert space

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays

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  • We have attempted to explain the concepts which have been used and developed to model the stochastic dynamics of natural and biological systems. While the theory of stochastic differential equations and stochastic processes provide an attractive framework with an intuitive appeal to many problems with naturally induced variations, the solutions to such models are an active area of research, which is in its infancy. Therefore, this book should provide a large number of areas to research further.

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  • This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes, and semigroup theory.

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  • Basic principles underlying the transactions of financial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical finance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of financial derivatives, a need for sophisticated computational technology has developed. For example, to price an American put, quantitative analysts have asked for the numerical solution of a free-boundary partial differential equation.

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  • In this research monograph, we explain the development of a mechanistic, stochastic theory of nonfickian solute dispersion in porous media. We have included sufficient amount of background material related to stochastic calculus and the scale dependency of diffusivity in this book so that it could be read independently.

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  • To introduce the ]orward-backward stochastic differential equations (FBS- DEs, for short), let us begin with some examples. Unless otherwise speci- fled, throughout the book, we let (~, •, {Ft)t_0, P) be a complete filtered probability space on which is defined a d-dimensional standard Brownian motion W(t), such that {5~t }t_0 is the natural filtration of W(t), augmented by...

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  • The mathematical theory now known as Malliavin calculus was first introduced by Paul Malliavin in [157] as an infinite-dimensional integration by parts technique. The purpose of this calculus was to prove the results about the smoothness of densities of solutions of stochastic differential equations driven by Brownian motion. For several years this was the only known application. Therefore, since this theory was considered quite complicated by many, Malliavin calculus remained a relatively unknown theory also among mathematicians for some time.

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  •      Phương trình vi phân thường (ODE) là phương trình vi phân trong đó hàm chưa biết là hàm 1 biến độc lập. Phương trình vi phân riêng phần (PDE) là phương trình vi phân trong đó hàm chưa biết là hàm của nhiều biến độc lập và các đạo hàm riêng của nó. delay differential equation (DDE) là phương trình vi phân trong đó giá trị đạo hàm của hàm chưa biết tại một thời điểm nào đó là tính theo giá trị của hàm tại một thời điểm khác.

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  • Stochastic Calculus of Variations (or Malliavin Calculus) consists, in brief, in constructing and exploiting natural differentiable structures on abstract probability spaces; in other words, Stochastic Calculus of Variations proceeds from a merging of differential calculus and probability theory. As optimization under a random environment is at the heart of mathematical finance, and as differential calculus is of paramount importance for the search of extrema, it is not surprising that Stochastic Calculus of Variations appears in mathematical finance.

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  • It has been mentioned in the Preface that the material of this book has been arranged in a way that should make it accessible to as wide a readership as possible. Prospective readers will have different backgrounds and objectives. The following four groups are suggestions to help use the book more efficiently.

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  • Modern game theory has evolved enormously since its inception in the 1920s in the works of Borel and von Neumann. The branch of game theory known as dynamic games descended from the pioneering work on differential games by R. Isaacs, L. S. Pontryagin and his school, and from seminal papers on extensive form games by Kuhn and on stochastic games by Shapley.

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  • Tuyển tập các báo cáo nghiên cứu về y học được đăng trên tạp chí y học Critical Care giúp cho các bạn có thêm kiến thức về ngành y học đề tài: Misdiagnosis and undiagnosis due to pattern similarity in Chinese medicine: a stochastic simulation study using pattern differentiation algorithm...

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  • Tuyển tập các báo cáo nghiên cứu về y học được đăng trên tạp chí y học Critical Care giúp cho các bạn có thêm kiến thức về ngành y học đề tài: Diagnostic accuracy of pattern differentiation algorithm based on Chinese medicine theory: a stochastic simulation study...

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Integral Inequality and Exponential Stability for Neutral Stochastic Partial Differential Equations with Delay

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: RELIABILITY OF DIFFERENCE ANALOGUES TO PRESERVE STABILITY PROPERTIES OF STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

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  • V an isometry, as in the theorem of Plancherel, is not just a weighted L2-norm on some measure space. This is due to the fact that the back transformation Z has a different expression on each branch, and this is caused by the ramification of the domain. It is not clear to us how one could find a family of generalized eigenfunctions leading to a spectral representation of A.

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  • We resolve these issues as follows. We show that a nonincreasing returns to scale (nrs) model is usually appropriate when modeling rational choice among investors. We show when multiple risk and return measures can justifiably be combined and identify some suitable measures. We show we need a nonlinear model to justify the assumption of convexity and to model diversification. We develop a method to approximate a solution to this model as accurately as needed using a sequence of linear models. Coherent measures of risk come up again and again in our discussion.

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  • When molecules are present in small numbers, such as is frequently the case in cells, the usual assumptions leading to differential rate equations are invalid and it is necessary to use a stochastic description which takes into account the randomness of reactive encounters in solution.

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