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We study the motion of an inertial microswimmer in a non-Newtonian environment with a finite memory and present the theoretical realization of an unexpected transition from its random self-propulsion to rotational (circular or elliptical)…
A dynamical treatment of Markovian diffusion is presented and several applications discussed. The stochastic interpretation of quantum mechanics is considered within this framework. A model for Brownian movement which includes second order…
Non-Markovian processes may arise in physics due to memory effects of environmental degrees of freedom. For quantum non-Markovianity, it is an ongoing debate to clarify whether such memory effects have a verifiable quantum origin, or…
The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation of its reduced density. The influence of the environment is incorporated through a mean-field which is both stochastic…
Markovian projections arise in problems where we aim to mimic the one-dimensional marginal laws of an It\^o semimartingale by using another It\^o process with Markovian dynamics. In applications, Markovian projections are useful in…
We study a non-linear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a non-linear diffusion predicts the existence of fronts as well as…
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…
Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…
Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a…
The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the…
Recent pioneering experiments on non-Markovian dynamics done e.g. for active matter have demonstrated that our theoretical understanding of this challenging yet hot topic is rather incomplete and there is a wealth of phenomena still…
Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…
Many physical, biological or social systems are governed by history-dependent dynamics or are composed of strongly interacting units, showing an extreme diversity of microscopic behaviour. Macroscopically, however, they can be efficiently…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
We consider any dynamical system that starts from a given ensemble of configurations and evolves in time until the system reaches a certain fixed stopping criterion, with the mean first-passage time the quantity of interest. We present a…
We analyze the non-Markovian spontaneous emission dynamics of a two-level test atom placed in a cavity formed by two atomic arrays in a waveguide quantum electrodynamics (QED) setup. We demonstrate a crossover from single-mode to multimode…
At the intersection of computation and cognitive science, graph theory is utilized as a formalized description of complex relationships and structures. Traditional graph models are often static, lacking dynamic and autonomous behavioral…
Memory effects in non-Markovian dynamics are often diagnosed either via quantum-correlation revivals or via non-monotonic classical information measures, yet a unified minimal framework comparing their ``backflow phases'' is still lacking.…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they generate, and stationary measures on that path-space. Such…