Related papers: Affine Diffusion Processes: Theory and Application…
Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have…
The weak-strong uniqueness for Maxwell--Stefan systems and some generalized systems is proved. The corresponding parabolic cross-diffusion equations are considered in a bounded domain with no-flux boundary conditions. The key points of the…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
In this paper, we consider a class of inhomogeneous semi-Markov processes directly based on intensity processes for marked point processes. We show that this class satisfies the semi-Markov properties defined elsewhere in the literature. We…
In this article we consider affine generalizations of the Merton jump diffusion model [Merton, J. Fin. Econ., 1976] and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be…
We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of canonical ensemble for a fixed number of particles which obey Bose-Einstein,…
We present a time change construction of affine processes with state-space $\mathbb{R}_+^m\times \mathbb{R}^n$. These processes were systematically studied in (Duffie, Filipovi\'c and Schachermayer, 2003) since they contain interesting…
We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
This study proposes a new stochastic model where the diffusion coefficient involves a state-dependent variable exponent function $p(\cdot)$. This new theoretically flexible framework generalizes the classical Cox-Ingersol-Ross model. The…
This paper improves a previously established test involving only coefficients to decide a priori whether or not non-trivial symmetries of a large class of space-time dependent diffusion processes on the real line exist. When the existence…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \alpha-stable random…
The evolution of a continuous time Markov process with a finite number of states is usually calculated by the Master equation - a linear differential equations with a singular generator matrix. We derive a general method for reducing the…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
ATSM are widely applied for pricing of bonds and interest rate derivatives but the consistency of ATSM when the short rate, r, is unbounded from below remains essentially an open question. First, the standard approach to ATSM uses the…
In this paper, we demonstrate through the use of matrix calculus a transparent analysis of fractional inhomogeneous Markov models for life insurance where transition matrices commute. The resulting formulae are intuitive matrix…
Second order recurrence of a $d$-dimensional diffusion with an additive Wiener process, with switching, and with one recurrent and one transient regime and constant switching intensities is established under suitable conditions. The…
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…
We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton--Watson processes. The class includes as specific cases the…