We construct a continuous bounded stochastic process (St)t2[0;1] which admits an equivalent martingale measure but such that the minimal martingale measure in the sense of Follmer and Schweizer does not exist. This example also answers (negatively) a problem posed by I. Karatzas, J. P. Lehozcky and S. E. Shreve as well as a problem posed C. Stricker.

In the paper we obtain some martingale versions of extrapolation theorems of Yano type by employing the technique of atomic decomposition in some Orlicz martingale spaces. Some variant extrapolation inequalities are also given. Mathematics subject classification (2010): Primary 60G42; Secondary 60G46.

Novel hidden thermodynamic structures have recently been uncovered during the investigation of nonequilibrium thermodynamics for multiscale stochastic processes. Here we reveal martingale structure a general functional inhomogeneous singularly perturbed diffusion processes under second-order averaging, where is defined as logarithmic Radon–Nykodim derivative between laws original process and co...

Unsupervised domain adaptation for object detectors addresses the problem of improving cross-domain robustness detection from label-rich to label-poor domains, which has been explored in many studies. However, one important issue terms when apply algorithm geospatial not fully considered literature. In this paper, we tackle detecting moment or change-point images changes based on conformal test...

For any discrete-time P–local martingale S there exists a probability measure Q ∼ P such that S is a Q–martingale. A new proof for this result is provided. This proof also yields that, for any ε > 0, the measure Q can be chosen so that dQ/dP ≤ 1 + ε.

We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod embedding which allows us to give a short proof of uniqueness.

We prove that for continuous stochastic processes S based on ( ;F;P) for which there is an equivalent martingale measureQ with square-integrable density dQ=dPwe have that the so-called "variance optimal" martingale measure Q for which the density dQ=dPhas minimal L(P)-norm is automatically equivalent to P. The result is then applied to an approximation problem arising in Mathematical Finance.

Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences (AR(1)). Further, we prove a martingale identity to be used in obtaining explicit bounds for the expectation of first passage times.

In the present paper we prove that for any 0 < p ≤ 2/3 there exists a martingale f in Hp such that the Marcinkiewicz-Fejér means of double conjugate Walsh-Kaczmarz-Fourier series of the martingale f is not uniformly bounded in the space Lp .

Freedman’s inequality is a martingale counterpart to Bernstein’s inequality. This result shows that the large-deviation behavior of a martingale is controlled by the predictable quadratic variation and a uniform upper bound for the martingale difference sequence. Oliveira has recently established a natural extension of Freedman’s inequality that provides tail bounds for the maximum singular val...