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The stochastic solution with Gaussian stationary increments is establihsed for the symmetric space-time fractional diffusion equation when $0 < \beta < \alpha \le 2$, where $0 < \beta \le 1$ and $0 < \alpha \le 2$ are the fractional…
We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…
We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths…
Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong Markov property of unique solutions are proven when the…
We consider the stochastic ranking process with space-time dependent unbounded jump rates for the particles. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic…
The Stochastic Backscatter Model involves the generation of a set of random variables characterised by prescribed correlations in space and time. These variables are obtained by smoothing an initially uncorrelated random field, which…
Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been…
This paper addresses finite sample stability properties of sequential Monte Carlo methods for approximating sequences of probability distributions. The results presented herein are applicable in the scenario where the start and end…
We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve…
In this paper we formalize, using the Nyquist-Shannon theorem, a fundamental temporal resolution limit for numerical experiments in complex systems. A consequence of this limit is aliasing, the introduction of spurious frequencies due to…
The logistic birth and death process is perhaps the simplest stochastic population model that has both density-dependent reproduction, and a phase transition, and a lot can be learned about the process by studying its extinction time,…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with…
We consider time-dependent space isotropic and time stationary spherical Gaussian random fields. We establish Chung's law of the iterated logarithm and solve the small probabilities problem. Our results depend on the high-frequency…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
This paper presents a novel algorithm solving the classic problem of generating a random sample of size s from population of size n with non-uniform probabilities. The sampling is done with replacement. The algorithm requires constant…
Stochastic Approximation (SA) is a popular approach for solving fixed-point equations where the information is corrupted by noise. In this paper, we consider an SA involving a contraction mapping with respect to an arbitrary norm, and show…
Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space…
We consider time-dependent space isotropic and time stationary spherical Gaussian random fields. We establish Chung's law of the iterated logarithm and solve the small probabilities problem. Our results depend on the high-frequency…
Spatial-temporal Gaussian process regression is a popular method for spatial-temporal data modeling. Its state-of-art implementation is based on the state-space model realization of the spatial-temporal Gaussian process and its…