Related papers: On jump-diffusion processes with regime switching:…

Let $L$ be a multidimensional L\'evy process under $P$ in its own filtration. The $f^q$-minimal martingale measure $Q_q$ is defined as that equivalent local martingale measure for $\mathcal {E}(L)$ which minimizes the $f^q$-divergence…

Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…

In many real-world scenarios, the underlying random fluctuations are non-Gaussian, particularly in contexts where heavy-tailed data distributions arise. A typical example of such non-Gaussian phenomena calls for L\'evy noise, which…

In the present paper we obtain sufficient conditions for the existence of equivalent martingale measures for L\'{e}vy-driven moving averages and other non-Markovian jump processes. The conditions that we obtain are, under mild assumptions,…

We study exponential Levy models with change-point which is a random variable, independent from initial Levy processes. On canonical space with initially enlarged filtration we describe all equivalent martingale measures for change-point…

Transfer entropy has been used to quantify the directed flow of information between source and target variables in many complex systems. While transfer entropy was originally formulated in discrete time, in this paper we provide a framework…

We study a stochastic system of $N$ interacting particles which models bimolecular chemical reaction-diffusion. In this model, each particle $i$ carries two attributes: the spatial location $X_t^i\in \mathbb{T}^d$, and the type $\Xi_t^i\in…

We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…

We consider a diffusion process $X$ in a random L\'{e}vy potential $\mathbb{V}$ which is a solution of the informal stochastic differential equation \begin{eqnarray*}\cases{dX_t=d\beta_t-{1/2}\mathbb{V}'(X_t) dt,\cr X_0=0,}\end{eqnarray*}…

The specific relative entropy, introduced by N. Gantert, allows to quantify the discrepancy between the laws of potentially mutually singular measures. It appears naturally as the large deviations rate function in a randomized version of…

We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [arXiv:1408.0628]. The system is a natural generalization of the coalescing Brownian motions. The main difference is that…

Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…

Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…

In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal…

This paper is about Girsanov's theory. It (almost) doesn't contain new results but it is based on a simplified new approach which takes advantage of the (weak) extra requirement that some relative entropy is finite. Under this assumption,…

Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…

The extension of thermodynamic principles to active matter remains a challenge due to the non-equilibrium nature inherent to active systems. In this study, we introduce a framework to assess entropy in our minimal macroscopic experiment…

This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…

This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…

We investigate the Poisson regression method for Markov and semi-Markov jump processes from a nonparametric angle, allowing the lengths of the time and duration intervals in the partition to vary with the number of observations. Imposing no…