Related papers: Martingale representations in progressive enlargem…
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,…
Given a reference filtration $\mathbb{F}$, we develop in this work a generic method for computing the semimartingale decomposition of $\mathbb{F}$-martingales in some specific enlargements of $\mathbb{F}$. This method is then applied to the…
Stricker's theorem states that a Gaussian process is a semimartingale in its natural filtration if and only if it is the sum of an independent increment Gaussian process and a Gaussian process of finite variation, see [1983, Z. Wahrsch.…
We provides some useful estimates for solving martingale representation problem under G-expectations. We also study the corresponding conditions for the existence and uniqueness.
The global weak martingale solution is built through a four-level approximation scheme to stochastic compressible active liquid crystal system driven by multiplicative noise in a smooth bounded domain in $\mathbb{R}^{3}$ with large initial…
We study general properties for the family of stochastic processes with polynomial regression property, that is that every conditional moment of the process is a polynomial. It turns out that then there exists a family of polynomial…
The martingale part in the semimartingale decomposition of a Brownian motion with respect to an enlargement of its filtration, is an anticipative mapping of the given Brownian motion. In analogy to optimal transport theory, we define causal…
We show that a large class of 1D first-order conservation PDEs can be probabilistically represented using multi-type branching processes. The representation holds when the initial conditions are linear combinations of negative exponentials.…
By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated…
We show the existence of superprocesses in a random medium with location dependent branching. Technically, we make use of a duality relation to establish the uniqueness of the martingale problem and to obtain the moment formulas.
In this paper, we obtain sufficient conditions in terms of projective criteria under which the partial sums of a stationary process with values in ${\mathcal{H}}$ (a real and separable Hilbert space) admits an approximation, in…
Two aspects of noncolliding diffusion processes have been extensively studied. One of them is the fact that they are realized as harmonic Doob transforms of absorbing particle systems in the Weyl chambers. Another aspect is integrability in…
We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…
We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer decomposition of projected local…
In this paper we show that stationary and non-stationary multivariate continuous-time ARMA (MCARMA) processes have the representation as a sum of multivariate complex-valued Ornstein-Uhlenbeck processes under some mild assumptions. The…
We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…
We construct families of rational functions $f \colon \bP^1_k \to \bP^1_k$ of degree $d \geq 2$ over a perfect field $k$ whose associated fixed-point processes fail to be martingales. Conversely, for any normal variety $X \subset…
We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are obtained by obtained by computing a directional derivative of the weak…
In the first part of this paper we give easy and intuitive proofs for the small value probabilities of the martingale limit of a supercritical Galton-Watson process in both the Schr\"oder and the B\"ottcher case. These results are…
We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees).…