AP calculus formula sheetAP CALCULUS Stuff You MUST Know Cold BASIC DERIVATIVES d n x = nx n −1 dx d ( sin( x )) = cos( x ) dx d ( cos( x )) = − sin( x ) dx d ( tan( x ) ) = sec2 ( x ) dx d ( cot( x ) ) = − csc2 ( x ) dx d ( sec( x ...
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We develop a stochastic calculus of divergence type with respect to the fractional Brownian sheet (fBs) with any Hurst parameters in and beyond the fractional scale. We define stochastic integration in the extended Skorohod sense, and derive It and Tanaka formulas. In the case of Gaussian fields...
We establish a version of the Feynman-Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the Feynman-Kac formula is a weak solution of the stochastic heat equa...