A Generalized Ito Formula
Kenneth L. Kuttler, Ji Li
TL;DR
This paper develops a generalized Ito formula suitable for singular or degenerate stochastic partial differential equations, extending previous formulas and establishing existence results for such complex equations.
Contribution
It introduces a generalized Ito formula applicable to a broader class of stochastic PDEs, including singular and degenerate cases, and proves an existence theorem for these equations.
Findings
Generalized Ito formula for singular and degenerate stochastic PDEs
Existence theorem for specific classes of stochastic equations
Examples demonstrating the application of the generalized formula
Abstract
An Ito formula is developed in a context consistent with the development of abstract existence and unique- ness theorems for nonlinear stochastic partial differential equations, which are singular or degenerate. This is a generalization of an earlier Ito formula for Gelfand triples. After this, an existence theorem is presented for some singular and degenerate stochastic equations followed by a few examples.
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Taxonomy
TopicsStochastic processes and financial applications · Probabilistic and Robust Engineering Design · Nonlinear Differential Equations Analysis