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Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary…

Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…

We consider a Markov process on a Riemannian manifold, which solves a stochastic differential equation in the interior of the manifold and jumps according to a deterministic reset map when it reaches the boundary. We derive a partial…

We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing.…

We present a theoretical investigation of the stochastic dynamics of a damped particle in a tilted periodic potential with a double well per period. By applying the matrix continued fraction technique to the Fokker-Planck equation in…

Let $\mathbb{F}$ be a filtration and $\tau$ be a random time. Let $\mathbb{G}$ be the progressive enlargement of $\mathbb{F}$ with $\tau$. We study the validity of the following formula, called optional splitting formula : For any…

In this article the almost semi-continuous step-process $\xi (t)$ is considered. The conditional characteristic functions of the jumps of $\xi (t)$ have the form $\mathrm{E} [ e^{i\alpha \xi_k}/\xi_k>0 ]=c(c-i\alpha)^{-1}$. For such…

A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…

Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…

We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…

We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically…

We study a triple of stochastic processes: a Wiener process $W_t$, $t \geq 0$, its running maxima process $M_t=\sup \{W_s: s \in [0,t]\}$ and its running minima process $m_t=\inf \{W_s: s \in [0,t]\}$. We derive the analytical formulas for…

The mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian alpha-stable type Levy motions. Both deterministic quantities are characterized by…

We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…

The goal of this work is to formally abstract a Markov process evolving in discrete time over a general state space as a finite-state Markov chain, with the objective of precisely approximating its state probability distribution in time,…

Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…

This paper is an extended and reworked version of a short course given by the author at ''Uzbekistan-Ukrainian readings in stochastic processes'', Tashkent-Kyiv, 2022, and was prepared for a special issue of ''Theory of stochastic…

A general method is proposed which allows one to estimate drift and diffusion coefficients of a stochastic process governed by a Langevin equation. It extends a previously devised approach [R. Friedrich et al., Physics Letters A 271, 217…

This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…