相关论文: Memory and Anticipation: Two main theorems for Mar…

A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as…

Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli. Building on the relationship between inference and learning, we derive a synaptic plasticity…

In this paper we develop necessary conditions for optimality, in the form of the Pontryagin maximum principle, for the optimal control problem of a class of infinite dimensional evolution equations with delay in the state. In the cost…

In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…

We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…

One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…

Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…

A multi-type continuous state and continuous time branching process with immigration satisfying some moment conditions is identified as a pathwise unique strong solution of certain stochastic differential equation with jumps.

The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…

Markov switching models (MSMs) are probabilistic models that employ multiple sets of parameters to describe different dynamic regimes that a time series may exhibit at different periods of time. The switching mechanism between regimes is…

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…

Multi-agent systems can be successfully described by kinetic models, which allow one to explore the large scale aggregate trends resulting from elementary microscopic interactions. The latter may be formalised as collision-like rules, in…

We investigate the non-Markovian dynamics of two-state systems in structured reservoirs. We establish a connection between two theoretical quantum approaches, the pseudomodes [B. M. Garraway, Phys. Rev. A 55, 2290 (1997)] and the recently…

The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique…

In the 1960s, Shiryaev developed a Bayesian theory of change-point detection in the i.i.d. case, which was generalized in the beginning of the 2000s by Tartakovsky and Veeravalli for general stochastic models assuming a certain stability of…

In this paper we study jump-diffusion stochastic differential equations (SDEs) with a discontinuous drift coefficient and a possibly degenerate diffusion coefficient. Such SDEs appear in applications such as optimal control problems in…

Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…

This paper is concerned with a linear quadratic stochastic Stackelberg differential game with time delay. The model is general, in which the state delay and the control delay both appear in the state equation, moreover, they both enter into…

We study and develop the stochastic Markov reward model (sMRM), which extends the Markov chain where transition time/reward as modelled as random variables. Techniques are presented to enable computing first-passage time distributions (or…

We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained…