Related papers: Stochastic Integrals and Evolution Equations with …
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations - matrices - acting on the data are often not accessible directly…
We review here the development of the general formalism for the study of fermion propagation in the presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
Importance sampling (IS) and numerical integration methods are usually employed for approximating moments of complicated target distributions. In its basic procedure, the IS methodology randomly draws samples from a proposal distribution…
The study of multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined…
Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and…
For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be…
We study nonlinear stochastic partial differential equations with Wick-analytic type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fisher--KPP equations, stochastic Allen--Cahn,…
Two problems are addressed for the path of certain stochastic processes: a) do they define currents? b) are these currents of a classical type? A general answer to question a) is given for processes like semimartingales or with Lyons-Zheng…
We present a review on the state-of-the-art of the mathematical framework known as stochastic inflation, paying special attention to its derivation and giving references for the readers interested on results coming from the application of…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
In this note, we extend an evolutionary stochastic portfolio optimization framework to include probabilistic constraints. Both the stochastic programming-based modeling environment as well as the evolutionary optimization environment are…
In this paper a quantum mechanical phase space picture is constructed for coarse-grained free quantum fields in an inflationary Universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase…
Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…
The current interpretation of stochastic gradient descent (SGD) as a stochastic process lacks generality in that its numerical scheme restricts continuous-time dynamics as well as the loss function and the distribution of gradient noise. We…
In this paper, we introduce the idea of stochastic integrals with respect to an increasing process in the $G$-framework and extend $G$-It\^o's formula. Moreover, we study the solvability of the scalar valued stochastic differential…
Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
Stochastic birth-death processes are described as continuous-time Markov processes in models of population dynamics. A system of infinite, coupled ordinary differential equations (the so-called master equation) describes the time-dependence…