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We provide escape rates formulae for piecewise expanding interval maps with `random holes'. Then we obtain rigorous approximations of invariant densities of randomly perturbed metabstable interval maps. We show that our escape rates…
We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…
In a recent work \cite{BG}, given a collection of continuous semimartingales, authors derive a semimartingale decomposition from the corresponding ranked processes in the case that the ranked processes can meet more than two original…
This paper presents estimates for the distribution of the exit time from balls and short time asymptotics for measure metric Dirichlet spaces. The estimates cover the classical Gaussian case, the sub-diffusive case which can be observed on…
We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only…
In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each…
In a recent paper, K. Raschel and R. Garbit proved that the exponential decreasing rate of the probability that a random walk (with all exponential moments) stays in a $d$-dimensional orthant is given by the minimum on this orthant of the…
In this paper, we study the Lagrangian functions for a class of second-order differential systems arising from physics. For such systems, we present necessary and sufficient conditions for the existence of Lagrangian functions. Based on the…
The directional differentiability of the solution map of obstacle type quasi-variational inequalities (QVIs) with respect to perturbations on the forcing term is studied. The classical result of Mignot is then extended to the…
Invariance times are stopping times $\tau$ such that local martingales with respect to some reduced filtration and an equivalently changed probability measure, stopped before $\tau$ , are local martingales with respect to the original model…
Numerous studies grounded on Hawkes processes have been carried out in many fields including finance, biology and social network. Hawkes processes form a class of selfexciting simple point processes. In this article, we consider a general…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales),…
We present sufficient conditions, in terms of the jumping kernels, for two large classes of conservative Markov processes of pure-jump type to be purely discontinuous martingales with finite second moment. As an application, we establish…
We apply general moment identities for Poisson stochastic integrals with random integrands to the computation of the moments of Markovian growth-collapse processes. This extends existing formulas for mean and variance available in the…
We derive a forward partial integro-differential equation for prices of call options in a model where the dynamics of the underlying asset under the pricing measure is described by a -possibly discontinuous- semimartingale. A uniqueness…
The exit time statistics of experimental turbulent data is analyzed. By looking at the exit-time moments (Inverse Structure Functions) it is possible to have a direct measurement of scaling properties of the laminar statistics. It turns out…
We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…