Lp-Theory for the fractional time stochastic heat equation with an infinite-dimensional fractional Brownian motion

In this paper, we study the [Formula: see text]-theory of the fractional time stochastic heat equation [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] denotes the Caputo derivative of order [Formula: see text], and [Formula: see text] is a sequence of i.i.d. fractional Brownian motions with a same Hurst index [Formula: see text]. The integral with respect to fractional Brownian motion is the Skorohod integral. By using the Malliavin calculus techniques and fractional calculus, we obtain a generalized Littlewood–Paley inequality, and prove the existence and uniqueness of [Formula: see text]-solution to such equation.

ON MULTI-ASSET SPREAD OPTION PRICING IN A WICK–ITÔ–SKOROHOD INTEGRAL FRAMEWORK

We provide an elementary method for exploring pricing problems of one spread options within a fractional Wick–Itô–Skorohod integral framework. Its underlying assets come from two different interactive markets that are modelled by two mixed fractional Black–Scholes models with Hurst parameters, $H_{1}\neq H_{2}$, where $1/2\leq H_{i}<1$ for $i=1,2$. Pricing formulae of these options with respect to strike price $K=0$ or $K\neq 0$ are given, and their application to the real market is examined.

Stochastic Current of Bifractional Brownian Motion

We study the regularity of stochastic current defined as Skorohod integral with respect to bifractional Brownian motion through Malliavin calculus. Moreover, we similarly derive some results in the case of multidimensional multiparameter. Finally, we consider stochastic current of bifractional Brownian motion as a distribution in Watanabe spaces.

FORWARD INTEGRALS AND AN ITÔ FORMULA FOR FRACTIONAL BROWNIAN MOTION

We consider the forward integral with respect to fractional Brownian motion B(H)(t) and relate this to the Wick–Itô–Skorohod integral by using the M-operator introduced by Ref. 10 and the Malliavin derivative [Formula: see text]. Using this connection we obtain a general Itô formula for the Wick–Itô–Skorohod integralswith respect to B(H)(t), valid for [Formula: see text].