from classical to stochastic differential equations

... differential equations, and perhaps partial differential equations as well This is all too much to expect of undergrads But white noise, Brownian motion and the random calculus are wonderful topics, too ... trajectories of systems modeled by (ODE) not in fact behave as predicted: X(t) x0 Sample path of the stochastic differential equation Hence it seems reasonable to modify (ODE), somehow to include ... of these notes is to provide a rigorous interpretation for calculations like these, involving stochastic differentials Example According to Itˆ’s formula, the solution of the stochastic differential...

Ngày tải lên: 31/03/2014, 15:56

... differential equations, and perhaps partial differential equations as well This is all too much to expect of undergrads But white noise, Brownian motion and the random calculus are wonderful topics, too ... trajectories of systems modeled by (ODE) not in fact behave as predicted: X(t) x0 Sample path of the stochastic differential equation Hence it seems reasonable to modify (ODE), somehow to include ... of these notes is to provide a rigorous interpretation for calculations like these, involving stochastic differentials Example According to Itˆ’s formula, the solution of the stochastic differential...

Ngày tải lên: 08/04/2014, 12:24

... solutions to some stochastic hyperbolic differential equations Electron J Differential Equations 2009, 111:1-14 19 Da Prato G, Tudor C: Periodic and almost periodic solutions for semilinear stochastic ... solutions for neutral differential equations Nonlinear Anal RWA 2010, 11:3037-3044 16 Bezandry P, Diagana T: Existence of almost periodic solutions to some stochastic differential equations Appl Anal ... almost automorphic mild solutions to some semilinear abstract differential equations Semigroup Forum 2004, 69:80-86 14 Zhao Z-H, Chang Y-K, Nieto JJ: Almost automorphic and pseudo almost automorphic...

Ngày tải lên: 21/06/2014, 03:20

... blank AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, ... with equations with a special structure that simplifies the solution process Therefore we shall progress from very simple equations to more complex ones There is a common thread to all types of equations ... century by Hamilton Hamilton investigated the propagation of light He sought to derive the rules governing this propagation 26 First-order equations from a purely geometric theory, akin to Euclidean...

Ngày tải lên: 16/02/2014, 15:20

... Stochastic Mechanics Random Media Signal Processing and Image Synthesis Mathematical Economics and Finance Stochastic Optimization Stochastic Control Stochastic Models in Life Sciences Stochastic ... solutions of SDEs These tools and results provide the basis for the application and numerical solution of stochastic differential equations with jumps 1.1 Stochastic Processes Stochastic Process If ... assistance 1 Stochastic Differential Equations with Jumps Stochastic differential equations (SDEs) with jumps provide the most flexible, numerically accessible, mathematical framework that allows us to model...

Ngày tải lên: 19/02/2014, 22:20

... introduction to this topic must focus on methods suitable for computers But these methods often rely on deep analytical insight into the equations We must therefore take great care not to throw away ... adopt to such problems, even if these equations may be hard to handle by an analytical approach In Chapter 12 we give a brief introduction to the Fourier transform and its application to partial ... solution we seek from a differential equation is a function 1.1.1 Concepts We usually subdivide differential equations into partial differential equations (PDEs) and ordinary differential equations (ODEs)...

Ngày tải lên: 31/03/2014, 15:56

... leading to the concept of Ito integrals in Chapter III In Chapter IV we develop the stochastic calculus (the Ito formula) and in Chap- XVI ter V we use this to solve some stochastic differential equations, ... solution of a stochastic differential equation) leads to a simple, intuitive and useful stochastic solution, which is the cornerstone of stochastic potential theory Problem is an optimal stopping problem ... Problem is a stochastic version of F.P Ramsey’s classical control problem from 1928 In Chapter X we formulate the general stochastic control problem in terms of stochastic differential equations, ...

Ngày tải lên: 31/03/2014, 15:57

... a from Ω1 to Ω and the process W from Ω2 to Ω in the obvious way For any t ≥ 0, ω ∈ Ω, the matrix σt (ω) corresponds to a linear operator Rm → Rn Let ϕt (ω) be the m × m-matrix of the operator ... equations that not satisfy this condition The use of such equations is necessary, in particular, if we want a solution to be positive In this monograph, these equations are called singular stochastic ... diagrams to illustrate the statement of each example The first square in the diagram corresponds to weak existence; the second – to strong existence; the third – to uniqueness in law; the fourth – to...

Ngày tải lên: 08/04/2014, 12:25

Ngày tải lên: 08/04/2014, 12:25

Ngày tải lên: 08/04/2014, 12:25

... that is necessary to an understanding of the transition from classical to wave mechanics Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton–Jacobi equation; ... 1991), and we have chosen to present them in some detail in chapter 14, which is devoted to the transition from classical to quantum statistical mechanics (ii) The crisis of classical physics, however, ... need to be introduced to quantum theory and its foundations For this purpose, part I covers the basic material which is necessary to understand the transition from classical to wave mechanics: the...

Ngày tải lên: 24/04/2014, 17:11

... that is necessary to an understanding of the transition from classical to wave mechanics Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton–Jacobi equation; ... 1991), and we have chosen to present them in some detail in chapter 14, which is devoted to the transition from classical to quantum statistical mechanics (ii) The crisis of classical physics, however, ... need to be introduced to quantum theory and its foundations For this purpose, part I covers the basic material which is necessary to understand the transition from classical to wave mechanics: the...

Ngày tải lên: 24/04/2014, 17:11

... INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS This refreshing, introductory textbook covers standard techniques for solving ordinary differential equations, as well as introducing students to qualitative ... to make the transition from theory to practice Exercises are also provided to test and extend understanding; full solutions for these are available for teachers AN INTRODUCTION TO ORDINARY DIFFERENTIAL ... linear equations and the integrating factor 9.1 Constant coefficients 9.2 Integrating factors 9.3 Examples 9.4 Newton’s law of cooling Exercises 10 Two ‘tricks’ for nonlinear equations 10.1 Exact equations...

Ngày tải lên: 12/05/2014, 03:24

... that is necessary to an understanding of the transition from classical to wave mechanics Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton–Jacobi equation; ... 1991), and we have chosen to present them in some detail in chapter 14, which is devoted to the transition from classical to quantum statistical mechanics (ii) The crisis of classical physics, however, ... need to be introduced to quantum theory and its foundations For this purpose, part I covers the basic material which is necessary to understand the transition from classical to wave mechanics: the...

Ngày tải lên: 05/06/2014, 11:19

... differential equations, ” Journal of Mathematical Analysis and Applications, vol 318, no 2, pp 726–741, 2006 10 J J Nieto and D O’Regan, “Variational approach to impulsive differential equations, ” ... Chen, J J Nieto, and A Torres, “Analysis of a delayed epidemic model with pulse vaccination and saturation incidence,” Vaccine, vol 24, no 35-36, pp 6037–6045, 2006 J Li and J J Nieto, “Existence ... this paper, our aim is to study the existence of n distinct pairs of nontrivial solutions to the Dirichlet boundary problem for the second-order impulsive differential equations u t λh t, u t...

Ngày tải lên: 21/06/2014, 11:20

... Riccati equations and stability of stochastic linear systems with nonincreasing delays,” Functional Differential Equations, vol 4, no 3-4, pp 279–293, 1997 K Liu, Stability of Infinite Dimensional Stochastic ... reduces to Theorem B Two examples In this section, we give two examples to illustrate applications of Theorem 2.1 and Corollary 2.4 Example 3.1 Consider the following linear neutral stochastic ... gj t Then the zero solution of 2.3 is asymptotically stable if and only if s ds → ∞, as t → ∞ Very recently, Luo considered the following neutral stochastic differential equation: d x t −q t x...

Ngày tải lên: 21/06/2014, 23:20

... Stochastic Mechanics Random Media Signal Processing and Image Synthesis Mathematical Economics and Finance Stochastic Optimization Stochastic Control Stochastic Models in Life Sciences Stochastic ... solutions of SDEs These tools and results provide the basis for the application and numerical solution of stochastic differential equations with jumps 1.1 Stochastic Processes Stochastic Process If ... assistance 1 Stochastic Differential Equations with Jumps Stochastic differential equations (SDEs) with jumps provide the most flexible, numerically accessible, mathematical framework that allows us to model...

Ngày tải lên: 28/06/2014, 17:20

... introduction to this topic must focus on methods suitable for computers But these methods often rely on deep analytical insight into the equations We must therefore take great care not to throw away ... adopt to such problems, even if these equations may be hard to handle by an analytical approach In Chapter 12 we give a brief introduction to the Fourier transform and its application to partial ... solution we seek from a differential equation is a function 1.1.1 Concepts We usually subdivide differential equations into partial differential equations (PDEs) and ordinary differential equations (ODEs)...

Ngày tải lên: 29/06/2014, 16:20

... of stochastic differential equations with discontinuous drift The aim of the present paper is to investigate the weak order of the Euler-Maruyama approximation for stochastic differential equations ... Numerically Solving Stochastic Dierential Equations with Discontinuous Coefficient Stoch Proc Appl , 76, 33–44 [3] Cherny, A and Engelbert, H-J (2005) Singular Stochastic Differential Equations Lecture ... boundary Stochastic Process Appl., 68(2), 285-302 [28] Talay, D and Tubaro, L (1990) Expansion of the global error for numerical schemes solving stochastic differential equations Stochastic...

Ngày tải lên: 14/10/2015, 07:53

... Numerical Solution of Stochastic Differential Equations Springer Ngo, H-L and Taguchi, D (2013) Strong rate of convergence for the EulerMaruyama approximation of stochastic differential equations with ... of stochastic integral equations Math USSR Sb 39, 387– 403 19 Yamada, T., Watanabe, S (1971) On the uniqueness of solutions of stochastic differential equations, Journal of Mathematics of Kyoto ... Euler-Maruyama scheme for stiff stochastic equations, in Stochastic Analysis and Related Topics V: The Silvri Workshop, Progr Probab 38, H Koerezlioglu, ed., Birkhauser, Boston, 183–202 Hutzenthaler,...

Ngày tải lên: 14/10/2015, 07:58