Results 1 to 10 of about 15,346 (67)
On the Quadratic Variation of Two-Parameter Continuous Martingales
Annals of Probability, 1984 Let M={M(z),z∈[0,1]2} be a two-parameter square integrable continuous martingale. We prove the sample continuity of the quadratic variation of M using an Ito's differentiation formula for M2.
D Nualart
exaly +5 more sources
r-variations for two-parameter continuous martingales and itô's formula
Stochastic Processes and Their Applications, 1989 Let \(M=\{M_ z;z\in [0,1]^ 2\}\) be a two-parameter continuous martingale bounded in \(L^ 4\), and suppose that f is a real-valued function of class \(C^ 4\) such that \(f(0)=0\). The aim of this paper is to establish an Itô's formula of the type \[ f(M_ z)=\sum^{4}_{r=1}(r!)^{-1}\int_{[0,z]}f^{(r)}(M_ u)d\mu^ r_ M(u), \] where the processes \(\mu^ r_ ...
exaly +3 more sources
A stochastic calculus for continuous N-parameter strong martingales
Stochastic Processes and Their Applications, 1985 Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale with respect to an increasing family of \(\sigma\)-fields satisfying the conditional independence property introduced by \textit{R. Cairoli} and \textit{J. B. Walsh}, Acta Math. 134, 111-183 (1975; Zbl 0334.60026).
Peter Imkeller
exaly +3 more sources
Local Time for Two-Parameter Continuous Martingales with Respect to the Quadratic Variation
Annals of Probability, 1988 The author studies the local time for two-parameter continuous martingales M as a density of the ``measure of sojourn time'' with respect to the quadratic variation \(\). First she shows that there exists a process \(\{L(x,s,t);\) \(x\in {\mathbb{R}}\setminus \{0\},\) \((s,t)\in {\mathbb{R}}^ 2_+\}\) satisfying the occupation density formula and which ...
exaly +4 more sources
A stochastic card balance management problem with continuous and batch-type bilateral transactions
Operations Research Perspectives, 2023 We study a stochastic continuous-review card balance management problem with two transaction patterns, namely, continuous and batch-type bilateral transactions, both in a Markovian environment.
Yonit Barron
doaj +1 more source
On representation and regularity of continuous parameter multivalued martingales [PDF]
Proceedings of the American Mathematical Society, 1998 Summary: We study multivalued martingales in continuous time. First we show that every multivalued martingale in continuous time can be represented as the closure of a sequence of martingale selections. Then we prove two results concerning the càdlàg modifications of continuous time multivalued martingales, in Kuratowski-Mosco convergence and in ...
Dong, Wenlong, Wang, Zhenpeng
openaire +2 more sources
Continuous-Parameter Martingales
Journal of Multivariate Analysis, 2002 The second part of this book starts with a continuous-parameter extension of the discrete-parameter theory of Chapter 1. Our use of the term “extension” is quite misleading. Indeed, we will quickly find that in order to carry out these “extensions,” one needs a good understanding of the regularity of the sample functions of multiparameter stochastic ...
Edgar, Gerald A, Sucheston, Louis
openaire +2 more sources
On compact Itô's formulas for martingales of mc4 [PDF]
, 1990 We prove that the class mc4 of continuous martingales with parameter set [0, 1] 2, bounded in L4, is included in the class of semi-martingales S∞c(Lo(P)) defined by'Allain in [A]. As a consequence we obtain a compact Itô's formula. Finally we relate this
Jolis Giménez, Maria
core +2 more sources
Doob's maximal identity, multiplicative decompositions and enlargements of filtrations [PDF]
, 2006 In the theory of progressive enlargements of filtrations, the supermartingale $Z_{t}=\mathbf{P}(g>t\mid \mathcal{F}_{t}) $ associated with an honest time g, and its additive (Doob-Meyer) decomposition, play an essential role. In this paper, we propose an
Nikeghbali, A., Yor, M.
core +2 more sources
Self-dual continuous processes [PDF]
, 2012 The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as their stochastic ...
Rheinländer, Thorsten, Schmutz, Michael
core +2 more sources