2018/12/23 by Nielsen, Lars Tyge
#60-01 #60G05 #60G07 #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR)
paper · doi:10.48550/arxiv.1812.09637
This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable processes to the space of continuous adapted processes. It is characterized in terms of two properties: (1) how the stochastic integrals of simple processes are calculated and (2) how these integrals converge in probability when the time integrals of the squared integrands converge in probability.