Absolute continuity and singularity of two probability measures on a filtered space

滤波空间上概率测度相互绝对连续性的刻画

A characterization of mutual absolute continuity of probability measures on a filtered space

该研究给出滤波空间上概率测度相互绝对连续性的新刻画，引入鞅极限M度量测度尾部相似性，证明其几乎必然等于1是相互绝对连续的充要条件，并将结果应用于随机变量族和过程。

Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process

In this paper we study mutual absolute continuity and singularity of probability measures on the path space which are induced by an isotropic stable Lévy process and the purely discontinuous Girsanov transform of this process. We also look at the problem of finiteness of the relative entropy of these measures. An important tool in the paper is the question under which circumstances the a.s. finiteness of an additive functional at infinity implies the finiteness of its expected value.

On Absolute Continuity and Singularity of Multidimensional Diffusions

Consider two laws \(P\) and \(Q\) of multidimensional possibly explosive diffusions with common diffusion coefficient \(\mathfrak{a}\) and drift coefficients \(\mathfrak{b}\) and \(\mathfrak{b} + \mathfrak{a} \mathfrak{c}\), respectively, and the law \(P^\circ\) of an auxiliary diffusion with diffusion coefficient \(\langle \mathfrak{c},\mathfrak{a}\mathfrak{c}\rangle^{-1}\mathfrak{a}\) and drift coefficient \(\langle \mathfrak{c}, \mathfrak{a}\mathfrak{c}\rangle^{-1}\mathfrak{b}\). We show that \(P \ll Q\) if and only if the auxiliary diffusion \(P^\circ\) explodes almost surely and that \(P\…

Reflected BSDEs on Filtered Probability Spaces

We study the problem of existence and uniqueness of solutions of backward stochastic differential equations with two reflecting irregular barriers, $L^p$ data and generators satisfying weak integrability conditions. We deal with equations on general filtered probability spaces. In case the generator does not depend on the $z$ variable, we first consider the case $p=1$ and we only assume that the underlying filtration satisfies the usual conditions of right-continuity and completeness. Additional integrability properties of solutions are established if $p\in(1,2]$ and the filtration is quasi-le…

Absolute continuity and singularity of Palm measures of the Ginibre point process

We prove a dichotomy between absolute continuity and singularity of the Ginibre point process $\mathsf{G}$ and its reduced Palm measures $\{\mathsf{G}_{\mathbf{x}}, \mathbf{x} \in \mathbb{C}^{\ell}, \ell = 0,1,2\dots\}$, namely, reduced Palm measures $\G_{\mathbf{x}}$ and $\G_{\mathbf{y}}$ for $\mathbf{x} \in \mathbb{C}^{\ell}$ and $\mathbf{y} \in \mathbb{C}^{n}$ are mutually absolutely continuous if and only if $\ell = n$; they are singular each other if and only if $\ell \not= n$. Furthermore, we give an explicit expression of the Radon-Nikodym density $d\G_{\mathbf{x}}/d \G_{\mathbf{y}}$ fo…

反应性赌博可能产生反效果： ruin概率随着p增加而增加，初始财富呈Hölder连续

Survival probability in reactive gambling: monotonicity, singularity, and Hölder continuity

该研究探讨了反应性赌博策略的反效果，证明当p<1/2且初始财富x>2时，赌徒有正概率存活，且破产概率随p增加而增加，但对x呈现奇异的Hölder连续性。