论文信息 - Functionals of diffusion processes as stochastic integrals

Functionals of diffusion processes as stochastic integrals

Let be a standard d-dimensional Brownian motion and L a smooth functional on the space C = Cd[0, 1] of continuous functions from [0,1] to Rd, such that Denote Then is a square integrable martingale which can be represented as a stochastic integral; consequently the random variable has the representation For Fréchet differentiable functions L, Clark(1) gave the following formula for the integrand e:

Mark H. A. Davis

[1] U. Haussmann. On the integral representation of functionals of ltd processest , 1980 .

[2] U. Haussmann. Functionals of Itô Processes as Stochastic Integrals , 1978 .

[3] Avner Friedman,et al. Stochastic Differential Equations , 1975 .

[4] J. M. Clark,et al. The Representation of Functionals of Brownian Motion by Stochastic Integrals , 1970 .

[5] Michel Loève,et al. Probability Theory I , 1977 .