2014/11/19 by María J. Garrido–Atienza, Garrido-Atienza, María J., Kening Lu +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1411.5237
openalex publication_date 2014/11/19 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In this article we are concerned with the study of the existence and\nuniqueness of pathwise mild solutions to evolutions equations driven by a\nH "older continuous function with H "older exponent in (1/3,1/2). Our\nstochastic integral is a generalization of the well-known Young integral. To be\nmore precise, the integral is defined by using a fractional integration by\nparts formula and it involves a tensor for which we need to formulate a new\nequation. From this it turns out that we have to solve a system consisting in a\npath and an area equations. In this paper we prove the existence of a unique\nlocal solution of the system of equations. The results can be applied to\nstochastic evolution equations with a non-linear diffusion coefficient driven\nby a fractional Brownian motion with Hurst parameter in (1/3,1/2], which is\nparticular includes white noise.\n