New classes of processes in stochastic calculus for signed measures

2012/07/10 by Fulgence Eyi Obiang, Obiang, Fulgence Eyi, Youssef Ouknine +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #advanced mathematical theories #math.PR

paper · pdf · doi:10.48550/arxiv.1207.2281

23 pages. arXiv admin note: text overlap with arXiv:math/0505515

arxiv created 2012/07/10 · openalex publication_date 2012/07/10 · arxiv updated 2012/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let us consider a signed measure \Qv and a probability measure \Pv such that \Qv<<\Pv. Let D be the density of \Qv with respect to \Pv. H represents the set of zeros of D, g=0\veesupH. In this paper, we shall consider two classes of nonnegative processes of the form X_t=N_t+A_t. The first one is the class of semimartingales where ND is a cadlag local martingale and A is a continuous and non-decreasing process such that (dA_t) is carried by H∪\t: X_t=0\. The second one is the case where N and A are null on H and A_.+g is a non-decreasing, continuous process such that (dA_t+g) is carried by \t: X_t+g=0\. We shall show that these classes are extensions of the class (∑) defined by A.Nikeghbali \citenik in the framework of stochastic calculus for signed measures.

Citations

• A class of remarkable submartingales

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