Stochastic differential equations in duals of nuclear spaces with some applications. Technical report, 30 September 1985-30 September 1986

Technical Report · Wed Oct 01 04:00:00 EDT 1986

OSTI ID:5669588

Kallianpur, G

These lectures aim at giving an elementary introduction to certain types of stochastic differential equations in infinite dimensional spaces. One lecture introduces countably Hilbertian Nuclear (CHN) spaces and give some examples to illustrate why these infinite dimensional spaces are convenient for the study of some practical problems, e.g., those occuring in stochastic evolutions. This lecture assumes a complete probability space with a right continuous filtration. It also assumes a given Countably Hilbertian nuclear space. Ornstein-Uhlenbeck stochastic differential equations on duals of nuclear spaces introduces a special class of linear stochastic differential equations with values in duals of nuclear spaces, namely Ornstein-Uhlenbeck type processes with a nuclear-valued martingale as a driving term. Weak Convergence of Solutions: the weak convergence of the solutions of to the corresponding stochastic differential equations driven by a Gaussian noise are considered. This last lecture gives an outline of recent works on stochastic evolution equations and nonlinear stochastic differential equations on the dual of a Countably Hilbert nuclear space.

• Research Organization: North Carolina Univ., Chapel Hill (USA). Center for Stochastic Precesses
• OSTI ID: 5669588
• Report Number(s): AD-A-186012/1/XAB; TR-158
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONAL ANALYSIS
HILBERT SPACE
MATHEMATICAL SPACE
MATHEMATICS
PROBABILITY
SPACE
STOCHASTIC PROCESSES