Nonlinear Young integrals via fractional calculus

Published 1 Mar 2015 in math.PR | (1503.00328v1)

Abstract: For H\"older continuous functions $W(t,x)$ and $\varphi_t$, we define nonlinear integral $\int_a^b W(dt, \varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.

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