Abstract: In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of ...

Dmitri Goloubentsev, Evgeny Lakshtanov and Vladimir Piterbarg explain in mathematical terms, and demonstrate using a simple example, how the automatic implicit function theorem, a special version of ...

ABSTRACT: In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the ...

Adjoint algorithmic differentiation is an efficient way to obtain financial instrument price derivatives with respect to the data inputs. Often the differentiation does not cover the full pricing ...

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ABSTRACT: In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the ...

Automatic differentiation is a transformation of the computational graph associated with the algorithmic implementation of a mathematical function. It breaks it down into atomistic primitive ...

Let $U$ open in $\bbR^{d+m}$. $\Phi:U\to \bbR^m$ is a $C^1$ map such that $\Phi'(p)$ is surjective (which means columns of the $m\times (d+m)$ matrix of $\Phi'(p ...