Backwards Itô–Henstock’s version of Itô’s formula

Abstract

In this paper, we formulate a version of Itô's formula for the backwards Itô-Henstock integral of an operator-valued stochastic process. Itô's formula is the stochastic analogue of the change of variable for deterministic integrals.

An Alternative Definition of the Itô Integral for the Hilbert-Schmidt-Valued Stochastic Process

“…If U is a separable Hilbert space, V = \BbbR , and \{ \lambda j , e j \} \infty j=1 is an eigensequence defined by Q \in L(U ), following the same argument as in [24,Example 4.14], we can show that…”

“…Before giving an example, we shall consider first the following simple form of a stochastic differential equation, see [24,Definition 4.13].…”

Stratonovich-Henstock integral for the operator-valued stochastic process

“…For the discussions on Fréchet derivatives, regulated mappings, primitives, billinear mappings, Riemann integrability on Banach spaces, and Taylor's formula, one may refer to [1], [4], [11], and [22].…”