Diffusion Processes and Partial Differential Equations

  title={Diffusion Processes and Partial Differential Equations},
  author={Kazuaki Taira},

Application to Diffusion Processes

After a review of the Gaussian transition function, a classical method of constructing Green functions for solving Poisson’s equation is modified to construct global solutions of the heat equation.

Stochastic Differential Equations

This chapter represents the core of the book. Building on the general theory introduced in previous chapters, stochastic differential equations (SDEs) are presented as a key mathematical tool for


This paper deals with some Feller semigroups acting on a particular weighted function space on [0;+1[ whose generators are degenerate elliptic second order differential operators. We show that these

Supplement to the paper "On the Oblique Derivative Problem for Diffusion Processes and Diffusion Equations with Hölder Continuous Coefficients"

On a C2 -domain in a Euclidean space, we consider the oblique derivative problem for a diffusion equation and assume the coefficients of the diffusion and boundary operators are Holder continuous. We

A remark on the existence of a diffusion process with non-local boundary conditions

It is known that a diffusion process on a domain D with smooth boundary is determined by a pair of analytical data (A, L), where A is a second order differential operator of elliptic type and L is a

On the existence of Feller semigroups with discontinuous coefficients II

This paper is devoted to the functional analytic approach to the problem of existence of Markov processes with Dirichlet boundary condition, oblique derivative boundary condition and first-order

Degenerate Evolution Equations in Weighted Continuous Function Spaces, Markov Processes and the Black-Scholes Equation — Part I

The present paper is mainly devoted to the study of initial boundary problems associated with a wide class of degenerate second-order differential operators on real intervals, in the framework of

Solvability and Regularity of Solutions for Some Classes of Elliptic Functional-Differential Equations

1. This review is devoted to the theory of boundary-value problems for some classes of elliptic functionaldifferential equations. Boundary-value problems for elliptic functional-differential

Oblique derivative problems and Feller semigroups with discontinuous coefficients

This paper is devoted to the functional analytic approach to the problem of existence of Markov processes with an oblique derivative boundary condition for second-order, uniformly elliptic

Logistic Dirichlet problems with discontinuous coefficients




On Boundary Conditions For Multidimensional Diffusion Processes

The problem considered in the paper is as follows: given an elliptical operator $\mathfrak{A}$ in a closed bounded region K, the most general boundary conditions are sought, which restrict

On the Support of Diffusion Processes with Applications to the Strong Maximum Principle

Abstract : Let a [0, infinity) X R(d) and S(d) and b: [0, infinity) X R(d) and R(d) be bounded continuous functions, where S(d) denotes the class of symmetric, nonnegative definite d X d matrices.

Sur l'existence de processus de diffusion

DÉFINITION 0.2. — Soit A le générateur infinitésimal d'un semi-groupe de Feller {Tj^o sur DOn dira que {Tj est un A-processus de diffusion sur D si A satisfait aux conditions suivantes : a) Au = Au