The It\\^o transform for a general class of pseudo-differential operators
Remi Leandre
TL;DR
This paper develops an Ito-type formula for semigroups generated by positive pseudo-differential operators, expanding stochastic calculus tools to a broader class of operators beyond those satisfying maximum principles.
Contribution
It introduces an Ito formula applicable to semigroups with generators that are positive pseudo-differential operators, not necessarily obeying maximum principles.
Findings
Derived an Ito formula for a new class of pseudo-differential operators.
Extended stochastic calculus to operators lacking maximum principle.
Provided theoretical foundation for future applications in stochastic analysis.
Abstract
We give an Ito type formula for a semi group whose generarator is a positive pseudo-differential operator which does not in general satisfies maximumu principle.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Numerical methods in inverse problems · Spectral Theory in Mathematical Physics