Related papers: Stochastic functional differential equations and s…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…
We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is…
It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Multi stage stochastic programs arise in many applications from engineering whenever a set of inventories or stocks has to be valued. Such is the case in seasonal storage valuation of a set of cascaded reservoir chains in hydro management.…
A generalization of the economic model of natural growth, which takes into account the power-law memory effect, is suggested. The memory effect means the dependence of the process not only on the current state of the process, but also on…
Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some…
The increasing availability of experimental data has intensified interest in calibrating stochastic models, raising fundamental questions about parameter identifiability. Structural identifiability determines whether parameters can be…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…
We present an adjoint sensitivity method for hybrid discrete -- continuous systems, extending previously published forward sensitivity methods. We treat ordinary differential equations and differential-algebraic equations of index up to two…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
A heuristic formula for 5-point approximation of the first derivative of an unknown function whose values are measured with an error at unequally spaced points is proposed. The derivative at a given point is calculated using the effective…
Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process…
A mathematical model for a one-phase change problem (particularly a Stefan problem) with a memory flux, is obtained. The hypothesis that the weighted sum of fluxes back in time is proportional to the gradient of temperature is considered.…