2007/10/12 by Sergey V. Lototsky, Lototsky, S. V., K. Stemmann +1
Economics, Econometrics and Finance · #60G15 #60H05 #60H07 #60H40 #Analysis of PDEs (math.AP) #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.0710.2506
openalex publication_date 2007/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic integrands. The problem is then to extend the definition to random integrands. An orthogonal decomposition of the chaos space of the random field, combined with the Wick product, leads to the \Ito-Skorokhod integral, and provides an efficient tool to study the integral, both analytically and numerically. For a Gaussian process, a natural definition of the integral follows from a canonical correspondence between random processes and a special class of random fields. Some examples of the corresponding stochastic differential equations are also considered.