On the integral representation of functionals of ltd processest
- 1 January 1980
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 3 (1-4), 17-27
- https://doi.org/10.1080/17442507908833134
Abstract
If z is the unique solution of the Itô equation and if L is a differentiable functional of the (continuous trajectories of z, then we show that where μ z is the function of bounded variation corresponding to the derivative of L(z), where ø is the fundamental matrix solutiion ogf the linearized version of the zbove Itô equation, and where is the algebra generated by w(s),s≦t.Keywords
This publication has 8 references indexed in Scilit:
- Functionals of Itô Processes as Stochastic IntegralsSIAM Journal on Control and Optimization, 1978
- On the Stochastic Maximum PrincipleSIAM Journal on Control and Optimization, 1978
- Nonexistence of strong nonanticipating solutions to stochastic DEs: implications for functional DEs, filtering, and controlStochastic Processes and their Applications, 1977
- General necessary conditions for optimal control of stochastic systemsPublished by Springer Nature ,1976
- Necessary Conditions for Continuous Parameter Stochastic Optimization ProblemsSIAM Journal on Control, 1972
- On the uniqueness of solutions of stochastic differential equationsKyoto Journal of Mathematics, 1971
- The Representation of Functionals of Brownian Motion by Stochastic IntegralsThe Annals of Mathematical Statistics, 1970
- On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of MeasuresTheory of Probability and Its Applications, 1960