Le theoreme de paul levy pour des mesures signees

Chávez, Juan Ruíz de

doi:10.1007/bfb0100048

Cited by 11 publications

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“…Meyer suggested to use signed measures in order to generalize the Paul Lévy's Theorem. This generalization was established by Ruiz de Chavez in [12] and completed by Beghdadi-Sakrani in [2]. The basis of stochastic calculus for signed measure theory has been established in both papers cited above.…”

Section: Definitionmentioning

confidence: 93%

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On the Study of Processes of $$\sum (H)$$ ∑ ( H ) and $$\sum _\mathrm{s}(H)$$ ∑ s ( H ) Classes

2015

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In papers by Yor, a remarkable class (Σ) of submartingales is introduced, which, up to technicalities, are submartingales (X t ) t≥0 whose increasing process is carried by the times t such that X t = 0. These submartingales have several applications in stochastic analysis: for example, the resolution of Skorokhod embedding problem, the study of Brownian local times and the study of zeros of continuous martingales.

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Section: Definitionmentioning

confidence: 93%

“…The basis of stochastic calculus for signed measure theory has been established in both papers cited above. Note that the authors of [12] and [2] did not use the same definition of martingale with respect to a signed measure. A martingale with respect to a signed measure was defined in [12] as follows.…”

Section: Definitionmentioning

confidence: 98%

On the Study of Processes of $$\sum (H)$$ ∑ ( H ) and $$\sum _\mathrm{s}(H)$$ ∑ s ( H ) Classes

2015

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“…. In a somewhat different vein, de Chávez [12] considers some processes obtained from Brownian motion by "formal" Girsanov transformation, i.e.,…”

Section: Introductionmentioning

confidence: 99%

Linear transformations of two independent Brownian motions and orthogonal decompositions of Brownian filtrations

Wu¹,

Yor²

2002

Publicacions Matemàtiques

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“…That is, the stochastic calculus when the measure space is governed, not by a probability measure, but by a general measure that can take positive and negative values (signed measure). In particular, a new class of processes satisfying Equation (1) was introduced in [7] where the authors provide a general framework and methods based on the tools of the martingale theory for signed measures developed by Ruiz de Chavez in [21]. This class is called, class Σ(H) and we shall define it in Section 3.The aim of this paper is to bring some contributions in frameworks of two above mentioned classes of stochastic processes.…”

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confidence: 99%

Some contributions to the study of stochastic processes of the classes and

et al. 2017

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This paper consists of two independent parts. In the first one, we contribute to the study of the class (Σ). For instance, we provide a new way to characterize stochastic processes of this class. We also present some new properties and solve the Bachelier equation. In the second part, we study the class of stochastic processes Σ(H). This class was introduced in [7] where from tools of the theory of martingales with respect to a signed measure of [21], the authors provide a general framework and methods for dealing with processes of this class. In this work, after developing some new properties, we embed a non-atomic measure ν in X, a process of the class Σ(H). More precisely, we find a stopping time T < ∞ such that the law of X T is ν. with respect to a signed measure; Hardy-Littlewood function MSC:60G07; 60G20; 60G46; 60G48 1 F. EYI-OBIANG et al dV t carried by the set {t ≥ 0 : X t = 0}. It plays an important role in martingale theory. For instance: the family of Azéma-Yor martingales, the resolution of Skorokhod's embedding problem, the study of Brownian local times. It also plays a key role in the study of zeros of continuous martingales. A large class containing all the previously mentioned processes is the class (Σ) whose definition is given in section 2. This class was introduced by Yor in [24] but some of its main properties were further studied in [6,12,13,14,15,16,17].Recently, the study of stochastic processes of the form of Equation (1) was generalized in the field of stochastic calculus for signed measures. That is, the stochastic calculus when the measure space is governed, not by a probability measure, but by a general measure that can take positive and negative values (signed measure). In particular, a new class of processes satisfying Equation (1) was introduced in [7] where the authors provide a general framework and methods based on the tools of the martingale theory for signed measures developed by Ruiz de Chavez in [21]. This class is called, class Σ(H) and we shall define it in Section 3.The aim of this paper is to bring some contributions in frameworks of two above mentioned classes of stochastic processes. More precisely, the Section 2 is dedicated to the study of the class (Σ) and Section 3 is reserved to the study of the class Σ(H). In particular, in Section 2, we shall provide a new characterization of processes of class (Σ). We give also a new solution of Bachelier equation. In Section 3, we prove the following estimates for processes of the class Σ(H), generalizing a well known result for the pair (X t , A t ) and for random variable A ∞ where X is a positive submartingale of the class (Σ) and A its non-decreasing process:

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Le theoreme de paul levy pour des mesures signees

Cited by 11 publications

References 0 publications

On the Study of Processes of $$\sum (H)$$ ∑ ( H ) and $$\sum _\mathrm{s}(H)$$ ∑ s ( H ) Classes

On the Study of Processes of $$\sum (H)$$ ∑ ( H ) and $$\sum _\mathrm{s}(H)$$ ∑ s ( H ) Classes

Linear transformations of two independent Brownian motions and orthogonal decompositions of Brownian filtrations

Some contributions to the study of stochastic processes of the classes and

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