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The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
In this paper we shall establish an existence and uniqueness result for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst…
In this paper, we focus on multiple sampling problems for the estimation of the fractional Brownian motion when the maximum number of samples is limited, extending existing results in the literature in a non-Markovian framework. Two classes…
In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of…
This paper contributes to the study of stochastic processes of the class $(\Sigma)$. First, we extend the notion of the above-mentioned class to c\`adl\`ag semi-martingales, whose finite variational part is considered c\`adl\`ag instead of…
In this paper we consider the classical differential equations of Hodgkin and Huxley and a natural refinement of them to include a layer of stochastic behavior, modeled by a large number of finite-state-space Markov processes coupled to a…
In this paper we prove a viability result for multidimensional, time dependent, stochastic differential equations driven by fractional Brownian motion with Hurst parameter1/2 < H < 1, using pathwise approach. The sufficient condition is…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
Stochastic differential equations (sdes) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes…
The construction of stochastic solutions is a powerful method to obtain localized solutions in configuration or Fourier space and for parallel computation with domain decomposition. Here a stochastic solution is obtained for the…
We introduce a dynamic approach to probabilistic forecast reconciliation at scale. Our model differs from the existing literature in this area in several important ways. Firstly we explicitly allow the weights allocated to the base…
Stochastic motion of a point -- known as Brownian motion -- has many successful applications in science, thanks to its scale invariance and consequent universal features such as Gaussian fluctuations. In contrast, the stochastic motion of a…
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of…
Many-body systems driven out of equilibrium can exhibit scaling flows of the quantum state. For a sudden quench to resonant interactions between particles we construct a new class of analytical scaling solutions for the time evolved wave…
The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is…