Uniqueness for Volterra-type stochastic integral equations
Leonid Mytnik, Thomas S. Salisbury
TL;DR
This paper investigates the uniqueness of solutions for a class of Volterra-type stochastic integral equations, especially when the noise coefficients are non-Lipschitz, highlighting their connection to degenerate stochastic PDEs.
Contribution
It introduces new results on uniqueness for Volterra-type stochastic integral equations with non-Lipschitz noise coefficients, linking them to degenerate stochastic PDEs.
Findings
Established uniqueness conditions for non-Lipschitz cases
Connected stochastic integral equations to degenerate SPDEs
Provided theoretical insights into solution behavior
Abstract
We study uniqueness for a class of Volterra-type stochastic integral equations. We focus on the case of non-Lipschitz noise coefficients. The connection of these equations to certain degenerate stochastic partial differential equations plays a key role.
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Taxonomy
TopicsStochastic processes and financial applications · Nonlinear Differential Equations Analysis · Stability and Controllability of Differential Equations