## 140 Citations

### Application to Diffusion Processes

- Mathematics
- 2014

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

- MathematicsAn Introduction to Continuous-Time Stochastic Processes
- 2021

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…

### MARKOV PROCESSES AND DIFFUSION EQUATIONS ON UNBOUNDED INTERVALS

- Mathematics
- 2001

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"

- Mathematics
- 1994

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

- Mathematics
- 1990

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

- Mathematics
- 2006

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

- Mathematics
- 2002

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

- Mathematics
- 2001

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

- Mathematics
- 2020

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…

## References

SHOWING 1-9 OF 9 REFERENCES

### On Boundary Conditions For Multidimensional Diffusion Processes

- Mathematics
- 1959

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

- Mathematics
- 1972

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

- Mathematics
- 1979

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…