相关论文: On time-inhomogeneous controlled diffusion process…

We consider optimal control problems for diffusion processes, where the objective functional is defined by a time-consistent dynamic risk measure. We focus on coherent risk measures defined by $g$-evaluations. For such problems, we…

This paper investigates the exit-time problem for time-inhomogeneous diffusion processes. The focus is on the small-noise behavior of the exit time from a bounded positively invariant domain. We demonstrate that, when the drift and…

We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. In the…

We prove a Carleman estimate for a one-dimensional parabolic equation which degenerates at one extremity of the domain and has a bounded, time dependent coefficient multiplying the diffusion term. Then we use the estimate to show the null…

We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical…

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

The solution to the infinite horizon optimal control problem for linear distributed time-delay systems is presented. The proposal is based on the use of the Cauchy solution for distributed time-delay systems. In contrast with previous…

We study an optimal control problem of McKean--Vlasov branching diffusion processes, in which the interaction term is determined by the marginal measure induced by all alive particles in the system. Accordingly, the value function is…

We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…

We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional L\'evy…

Deterministic optimal impulse control problem with terminal state constraint is considered. Due to the appearance of the terminal state constraint, the value function might be discontinuous in general. The main contribution of this paper is…

In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…

A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…

This paper studies {a} mixed singular/switching stochastic control problem for a multidimensional diffusion with multiples regimes on a bounded domain. Using probabilistic, partial differential equation (PDE) and penalization techniques, we…

This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production of the time-inhomogeneous process with respect to…

We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle…

In this note, we propose two different approaches to rigorously justify a pseudo-Markov property for controlled diffusion processes which is often (explicitly or implicitly) used to prove the dynamic programming principle in the stochastic…

We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…

We prove the dynamic programming principle for a class of diffusion processes controlled up to the time of exit from a cylindrical region $[0,T)\times G$. It is assumed that the functional to be maximized is in the Lagrange form with…

Let $B=(B_t)_{t\geq 0}$ be a standard Brownian motion. The main objective is to find a uniform (in time) control of the modulus of continuity of $B$ in the spirit of what appears in (Kurtz, 1978). More precisely, it involves the control of…