Transformations of Wiener measure and orthogonal expansions
| Autor: | Andrey A. Dorogovtsev, Georgii V. Riabov |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Applied Mathematics Probability (math.PR) 010102 general mathematics Mathematical analysis Statistical and Nonlinear Physics 01 natural sciences Measure (mathematics) 010104 statistics & probability symbols.namesake Change of measure Square-integrable function Wiener process FOS: Mathematics symbols 0101 mathematics Mathematics - Probability Mathematical Physics Mathematics |
| Zdroj: | Infinite Dimensional Analysis, Quantum Probability and Related Topics. 19:1650018 |
| ISSN: | 1793-6306 0219-0257 |
| DOI: | 10.1142/s0219025716500181 |
| Popis: | In this paper we study the structure of square integrable functionals measurable with respect to coalescing stochastic flows. The case of $L^2$ space generated by the process $\eta(\cdot)=w(\min(\tau,\cdot)),$ where $w$ is a Brownian motion and $\tau$ is the first moment when $w$ hits the given continuous function $g$ is considered. We present a new construction of multiple stochastic integrals with respect to the process $\eta.$ Our approach is based on the change of measure technique. The analogue of the It\^o-Wiener expansion for the space $L^2(\eta)$ is constructed. |
| Databáze: | OpenAIRE |
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