相关论文: Markov-modulated generalized Ornstein-Uhlenbeck pr…

We consider continuous time risk processes in which the claim sizes are dependent and non-identically distributed phase-type distributions. The class of distributions we propose is easy to characterize and allows to incorporate the…

It is known that the distribution of nonreversible Markov processes breaking the detailed balance condition converges faster to the stationary distribution compared to reversible processes having the same stationary distribution. This is…

Spatio-temporal modelling is an increasingly popular topic in Statistics. Our paper contributes to this line of research by developing the theory, simulation and inference for a spatio-temporal Ornstein-Uhlenbeck process. We conduct…

We have shown recently that a Markov process conditioned on rare events involving time-integrated random variables can be described in the long-time limit by an effective Markov process, called the driven process, which is given…

The quintic Ornstein-Uhlenbeck volatility model is a stochastic volatility model where the volatility process is a polynomial function of degree five of a single Ornstein-Uhlenbeck process with fast mean reversion and large vol-of-vol. The…

We conduct a preliminary analysis of a pairs trading strategy using the Ornstein-Uhlenbeck (OU) process to model stock price spreads. We compare this approach to a naive pairs trading strategy that uses a rolling window to calculate mean…

These notes give a summary of techniques used in large deviation theory to study the fluctuations of time-additive quantities, called dynamical observables, defined in the context of Langevin-type equations, which model equilibrium and…

The paper provides an overview of the theory and applications of risk-sensitive Markov decision processes. The term 'risk-sensitive' refers here to the use of the Optimized Certainty Equivalent as a means to measure expectation and risk.…

We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit…

We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…

The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two…

This paper focuses on rate-limited control of the generalized Ornstein-Uhlenbeck process where the control action can be either multiplicative or additive, and the noise variance can depend on the control action. We derive a lower bound on…

The purpose of this article is to derive the crossover from the Ornstein-Uhlenbeck process to energy solutions of the stochastic Burgers equation with characteristic operators given in terms of fractional operators, such as the regional…

We give a representation of the solution for a stochastic linear equation of the form $X_t=Y_t+\int_{(0,t]}X_{s-} \mathrm {d}{Z}_s$ where $Z$ is a c\'adl\'ag semimartingale and $Y$ is a c\'adl\'ag adapted process with bounded variation on…

This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…

We consider Ornstein-Uhlenbeck processes (OU-processes) associated to hypoelliptic diffusion processes on finite-dimensional Lie groups: let $ \mathcal{L} $ be a hypoelliptic, left-invariant ``sum of the squares''-operator on a Lie group $…

We study the stationary fluctuations of independent run-and-tumble particles. We prove that the joint densities of particles with given internal state converges to an infinite dimensional Ornstein-Uhlenbeck process. We also consider an…

In this paper we give few expressions and asymptotics of ruin probabilities for a Markov modulated risk process for various regimes of a time horizon, initial reserves and a claim size distribution. We also consider few versions of the ruin…

We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of…

In this paper the feasibility of funnel control techniques for the Fokker-Planck equation corresponding to a multi-dimensional Ornstein-Uhlenbeck process on an unbounded spatial domain is explored. First, using weighted Lebesgue and Sobolev…