关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Stochastic differential equations and diffusion processes

13. 벼잎선충의 약제처리 방법별 방제 효과

Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.

/pdf/multidimensional-stochastic-processes-as-rough-paths-5cpf00j8b4.pdf

Multidimensional Stochastic Processes as Rough Paths

We give a thorough description of the asymptotic property of the maximum likelihood estimator (MLE) of the skewness parameter of a Skew Brownian Motion (SBM). Thanks to recent results on the Central Limit Theorem of the rate of convergence of estimators for the SBM, we prove a conjecture left open that the MLE has asymptotically a mixed normal distribution involving the local time with a rate of convergence of order $1/4$. We also give a series expansion of the MLE and study the asymptotic behavior of the score and its derivatives, as well as their variation with the skewness parameter. In particular, we exhibit a specific behavior when the SBM is actually a Brownian motion, and quantify the explosion of the coefficients of the expansion when the skewness parameter is close to $-1$ or $1$.

Maximum likelihood estimator for skew Brownian motion: the convergence rate

https://hal.inria.fr/inria-00451193/document

Global solutions to rough dierential equations with

In this survey article, we present an overview of a large class of probabilistic representations of the fragmentation equation, and we develop and study the interconnections in between these representations. We focus on the stochastic process which represents the evolution of the mass of a typical particle which undergoes fragmentation in time. These probabilistic representations range from Markov chains to stochastic differential equations with jumps, and we aim at constructing how they are inter-related. In particular, we show how these representations can be used to develop easy to implement numerical methods. 

Probabilistic representations of fragmentation equations

In this article, we give a simple presentation of the theory of rough paths, that relies only on simple considerations on integrals along smooth paths and convergence of families of Holder continuous functions.

/pdf/rough-paths-an-introduction-using-classical-analysis-30knvfnu7s.pdf

Rough Paths: An Introduction Using Classical Analysis

In order to solve with a Monte Carlo method a parabolic (or elliptic) PDE with a transmission condition, we need to understand the behavior of the stochastic process when it reaches a point where this tranmission condition holds. In this article, we show that a process called the Skew Brownian motion can be helpful to understand how to deal with this kind of problem in a one-dimensional media.

https://hal.inria.fr/inria-00092418/document

Antoine Lejay

Papers

Maximum likelihood estimator for skew Brownian motion: the convergence rate

Global solutions to rough dierential equations with

Probabilistic representations of fragmentation equations

Rough Paths: An Introduction Using Classical Analysis

A probabilistic interpretation of the transmission conditions using the Skew Brownian motion